JP3447379B2 - A device for creating images with repetitive patterns - Google Patents

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention has a repeating pattern.
The present invention relates to an image creating apparatus, and more particularly, to a technique for forming a pattern having a natural fluctuation by utilizing a fractal theory.

[0002]

2. Description of the Related Art In recent years, an image generated and processed by using a computer has been found in every printed matter. In particular, the patterns found on building material products such as wallpaper and packaging of products are often created using computer graphics technology to some extent.
An image captured as digital data in a computer can be enlarged or reduced, and processing such as intentionally distorting the image can be freely performed. Very high, and a unique processing method is often used to aim for a special effect.

Such image information is information having a very large amount of data. Therefore, when applied to a printed matter having a very large area such as wallpaper, it is common to use a repeating pattern. For example, in the case of printing a wallpaper having a large area such as several meters × several tens of meters, if the image data of such a large area is actually prepared, the amount of data becomes enormous. The burden on the hardware becomes very heavy. Therefore,
For example, if a unit image of 1 m × 1 m is prepared and a plurality of unit images are arranged adjacent to each other in a plane, theoretically, wallpaper of any size can be printed. It will be possible. Moreover, since the image information actually handled in the computer is a unit image with a size of 1 m × 1 m, the load on the hardware is significantly reduced.

However, in this case, it is necessary to form a so-called repeatable pattern in which the boundary portions are continuously connected in the image prepared as the unit image. If the pattern of the boundary portion is discontinuous, the boundary line of each unit image is visually recognized, and a grid of 1 m × 1 m will appear as a pattern. Therefore, normally, at the stage of generating a pattern used as a unit image, consideration is given to the pattern at the boundary to be continuous, and a repeatable pattern is generated.

[0005]

[Problems to be Solved by the Invention] Contrary to the progress of science and technology, in recent years, a more naturally adapted lifestyle has been respected. For this reason, a more natural design is required for all industrial products such as building material products such as wallpaper and various product packages. However, the artificially designed texture using a computer or the like still has an artificial texture, and compared to all things in the natural world, the artificial discomfort cannot be eliminated. For example, it has been attempted to use a pseudo-grain or pseudo-grain pattern artificially generated by computer graphics technology as a wallpaper pattern. Awkward and artificial texture remains.

Therefore, in order to obtain a more natural pattern, the surface pattern of a natural wood board or a natural stone board is captured as digital data, and the digital data is processed to generate a wood pattern or a stone pattern to be printed on wallpaper or the like. The method of doing is also widely used. However, it is very difficult to produce a printed matter that completely expresses the natural texture. Further, as described above, when a repeating pattern is formed by arranging the unit images continuously, it is necessary to form a repeatable pattern such that the patterns at the boundary portions of the unit images are continuous. For this reason, even if the surface patterns of natural wood boards and natural stone boards are imported into the computer, it is necessary to artificially correct the boundary pattern, and the natural pattern cannot be used as it is as a printed matter. Can not.

Therefore, an object of the present invention is to provide an apparatus which has natural fluctuations and which creates an image formed by continuously arranging a repeating pattern.

[0008]

[Means for Solving the Problems]

(1) A first aspect of the present invention is a unit fractal grid in which a predetermined scalar value is self-similarly defined at each grid point in an image forming apparatus having a repeating pattern. A method for generating a repeatable unit fractal lattice in which each scalar value is defined so that the boundary portions of individual unit fractal lattices are continuously connected when a plurality of fractal lattices are arranged spatially, and this repeatable unit. By using each scalar value distributed in the unit fractal grid, a unit for generating a unit image composed of pixels distributed in a predetermined unit area, and spatially arranging the unit images spatially, And a means for generating a composite image in which a repeating pattern is expressed .
It is a thing.

(2) A second aspect of the present invention is, in an image creating apparatus having a repeating pattern, a two-dimensional unit fractal in which a predetermined scalar value is self-similarly defined at each lattice point on a two-dimensional plane. When a plurality of two-dimensional unit fractal lattices are arranged on a plane, a repeatable two-dimensional unit in which each scalar value is defined so that the boundary portions of the individual two-dimensional unit fractal lattices are continuously connected. means for generating a dimensional unit fractal grid, utilizing the scalar values distributed in the repeatable dimensional units in fractal grid, means for generating a unit image consisting of pixels distributed in a predetermined planar region, the By arranging a plurality of unit images on a plane, a unit for generating a composite image in which a planar repeating pattern is expressed is provided.
is there.

(3) A third aspect of the present invention is based on the above-mentioned second aspect .
In the apparatus for creating an image having a repetitive pattern according to the above aspect, a repeatable two-dimensional unit fractal grid is generated.
Means defines a 0th stage grid point having a predetermined scalar value at a predetermined position according to a setting operation from the outside, and a scalar value of the grid point defined up to the (i-1) th stage. Based on the above, the operation of giving a predetermined scalar value to the grid point defined in the i-th step is repeatedly executed until the parameter i reaches the predetermined value n while increasing the parameter i by 1 from the initial value 1 and In the task of giving a scalar value, when giving a predetermined scalar value to each grid point,
For the grid points on the first boundary side of the grid, give the same scalar value as the scalar value given for the grid point at the connection corresponding position on the second boundary side facing the first boundary side, and For the grid point on the third boundary side, the repeatable value is given by giving the same scalar value as that given to the grid point at the connection corresponding position on the fourth boundary side facing the third boundary side. It is designed to generate a two-dimensional unit fractal lattice.

(4) A fourth aspect of the present invention is the above-mentioned third aspect .
In the apparatus for creating an image having a repetitive pattern according to the above aspect, a repeatable two-dimensional unit fractal grid is generated.
Means for defining four grid points of the 0th stage having the same scalar value at each of four corner positions of the outer shape rectangle forming the outer shape of the grid according to the setting operation from the outside, and
-1) Recognize the minimum rectangle at the current stage that does not include the grid points defined up to the stage, and define it at the midpoint of each side of this minimum rectangle and the center point of this minimum rectangle at the i-th stage. A grid point to be generated is generated, and the grid point generated at the midpoint of each side is a random number in the scalar value of the two grid points defined up to the (i-1) th stage existing at the end point of the side. Gives a scalar value obtained by operating
For the grid points generated at the center point of the minimum rectangle, by applying random numbers to the scalar values of the four grid points defined up to the (i-1) th stage existing at the four corners of the minimum rectangle, By giving the obtained scalar value, the work of giving a predetermined scalar value to the grid point defined in the i-th stage is performed, and the above-mentioned work is performed while the parameter i is increased by 1 from the initial value 1 by a predetermined value. Value n
When the side of the minimum rectangle matches the first side of the outline rectangle in the above work, the grid point generated at the midpoint of the side of the minimum rectangle is the first side. When the side of the minimum rectangle matches the third side of the outline rectangle, the scalar value is the same as the scalar value given to the grid point at the connection corresponding position on the second side of the outline rectangle facing For the grid point generated at the midpoint of the side of the smallest rectangle, by giving the same scalar value as the scalar value given to the grid point of the connection corresponding position on the fourth side of the outer shape rectangle facing the third side , A repeatable two-dimensional unit fractal lattice is generated.

(5) A fifth aspect of the present invention is based on the above-mentioned second aspect .
In the apparatus for creating an image having a repeating pattern according to any one of aspects 4 to 4 , the unit for generating a unit image is arranged within a predetermined rectangular area at each grid point forming the repeatable two-dimensional unit fractal grid A unit image is generated by associating each distributed pixel with each pixel and defining a pixel value corresponding to the scalar value of the corresponding grid point for each pixel.

(6) A sixth aspect of the present invention is based on the above-mentioned second aspect .
In an apparatus for creating an image having a repeating pattern according to any one of the aspects 1 to 4, a repeatable two-dimensional unit fractal grid is generated.
The means for generating is the coordinate position (x, y) on the XY two-dimensional plane.
Hand a lattice point F (x, y) to generate a repeatable two-dimensional unit fractal lattices formed by arranging, and generates unit image
Stage, based on the first image P formed by arranging pixel P (x, y) having a predetermined pixel value to a coordinate position on the XY two-dimensional plane (x, y), a given pixel A pixel Q (x, y) having a value is assigned to a coordinate position (x,
Raw second image Q constituted by arranging y)
And has the function of generating the second image Q, the pixel Q (x, y) arranged at the coordinate position (x, y) is used to generate the second image Q.
The grid point F located at the coordinate position (x, y) with respect to
The displacement amount d corresponding to the scalar value defined for (x, y) is determined, and the pixel P (x + d, y) arranged at the coordinate position (x + d, y) is specified as a reference pixel, and this reference The pixel value Z of the pixel P (x + d, y) is converted into the pixel Q (x,
The second image Q is completed by adding it to y).

(7) A seventh aspect of the present invention is based on the above-mentioned second aspect .
In the method for producing a printed matter having a repeating pattern according to any one of aspects 1 to 4, a repeatable two-dimensional unit fractal grid is used.
The means for generating is a coordinate position (x,
A repeatable two-dimensional unit fractal grid in which grid points F (x, y) are arranged in y) is generated, and a unit image is generated.
Means for forming a wrinkled surface by displacing each point of a predetermined surface in a predetermined direction according to a scalar value of each grid point of the two-dimensional unit fractal grid, and a pixel having a predetermined pixel value is formed. A 3D stereoscopic image composed by arranging in XYZ 3D space is input , the 3D stereoscopic image is cut by the wrinkled surface, and pixels appearing on the cut surface are projected on a plane to form a unit. It is designed to generate an image.

(8) An eighth aspect of the present invention is, in an apparatus for creating an image having a repeating pattern, a fractal condition setting unit for setting conditions necessary for generating a unit fractal grid, and a unit fractal grid. Random number generator that generates random numbers to give fluctuations to the scalar value given to each grid point, the condition set in the fractal condition setting unit, and the random number generated by the random number generator. Thus, when a plurality of generated unit fractal grids are spatially arranged, the boundary values of the individual unit fractal grids are continuously connected when the scalar value calculation unit that calculates the scalar value to be given to each grid point is spatially arranged. like,
A scalar value diversion unit that diverts a scalar value to be given to a predetermined grid point of the boundary portion from a scalar value of another grid point,
By giving either a scalar value calculated by the scalar value calculation unit or a scalar value diverted by the scalar value conversion unit to each lattice point, a predetermined scalar value is self-similarly defined at each lattice point. A fractal grid generation unit that generates a unit fractal grid, a pattern condition setting unit that sets the conditions necessary to generate a unit pattern expressed as a printed matter, and a distribution in the unit fractal grid generated by the fractal grid generation unit A unit image composed of pixels distributed in a predetermined unit area is generated by a predetermined calculation based on each scalar value and the condition set in the pattern condition setting unit, and a plurality of unit images are spatially arranged. As a result, an image generating unit that generates a composite image in which a spatially repeating pattern is expressed is provided .

(9) A ninth aspect of the present invention is based on the above-mentioned eighth aspect .
In the apparatus for creating an image having a repetitive pattern according to this aspect, the fractal condition setting unit has a size of a unit fractal grid to be generated, a maximum half-amplitude value T, and four corners of an outer shape rectangle forming the outer shape of the grid. The fractal grid generating unit has a function of setting initial grid points having the same scalar value arranged at each position of and as a condition, and the fractal grid generation unit internally sets the midpoint and other grid points of two adjacent grid points. The function of defining a new grid point at the center point of the four grid points forming the minimum rectangle not included in the scalar value calculation unit gives it to the new grid point defined at the midpoint of the two grid points. As the power scalar value, the total value of the average value of the scalar values of the two lattice points and the number obtained by multiplying the random number generated by the random number generator by the maximum half-amplitude value T or its (1/2 ⁿ ) is used. 4 grid points As a scalar value to be given to the new grid points defined at the center point, four and the average value of the scalar values with the grid points, the maximum half-amplitude random numbers by the random number generator is generated value T or a (1/2 ⁿ ) And the total value of, and the scalar value diversion unit uses the generated unit fractal grids as a scalar value that should be diverted to the grid points of the boundary, The fractal grid generation unit defines a new grid point until the size set by the fractal condition setting unit is obtained by using the scalar value given to the grid point of another boundary part to be Repeatedly,
When the newly defined grid point is on the first side of the outline rectangle or the second side orthogonal to this, the scalar value diverting section gives the scalar value diverted to this grid point to newly define When the grid point is not on the first side or the second side, processing for giving the scalar value calculated by the scalar value calculation unit to this grid point is performed.

[0018]

[Operation] It is widely known that fractal figures are suitable for representing many things in the natural world. The feature of this fractal figure is that its complexity is always the same whether it is microscopic or macroscopic.
The shapes of coastlines, the shapes of trees and veins, the shapes of snowflakes, etc. found in the natural world are all typical of this fractal figure, and they are intricate even when viewed microscopically or macroscopically. It has a unique shape. Such a property is generally called self-similarity. The essence of fractal theory lies in this self-similarity, and a more general extension of this theory makes it possible to consider a fractal lattice in which a given scalar value is self-similarly defined at each lattice point. For example, the two-dimensional fractal lattice defines a predetermined scalar value for each lattice point arranged on a two-dimensional plane and gives a two-dimensional scalar field. In this two-dimensional scalar field, each scalar value changes spatially with natural fluctuations. In other words, this change pattern, whether microscopically or macroscopically, always has the same complexity, that is, self-similarity.

A general method for generating such a fractal lattice consists of the following steps. First, in the initial stage, lattice points each having a predetermined scalar value are defined. Next, based on these initial stage grid points,
First-stage grid points are generated, and a scalar value is determined for this first-stage grid point by a predetermined method based on the scalar value of the initial-stage grid point. Similarly, second-stage grid points are generated based on the first-stage grid points, and a predetermined method is performed for the second-stage grid points based on the scalar values of the first-stage grid points. Determine the scalar value with. By repeating the above steps, a large number of grid points are generated, and a scalar value is defined for each grid point.

In the process of generating such a fractal grid, the inventor of the present application adds a predetermined condition to the scalar value given to the grid point at the boundary portion, so to speak, so to speak, as a "repeatable unit fractal grid". We have found that we can generate fractal lattices. This "repeatable unit fractal lattice" is, in short, "a fractal lattice in which the boundary portions are continuously connected when spatially arranged in a plurality," in other words, "this unit fractal lattice". Is a fractal lattice in which the scalar field of the synthetic fractal lattice obtained by arranging a plurality of spatially is not disturbed by the boundary line of the unit fractal lattice.

Further, if the inventor of the present application generates a unit image based on this "repeatable fractal lattice", a pattern with natural fluctuation will be expressed in this unit image, and furthermore, this It was found that in a composite image obtained by spatially arranging a plurality of unit images, a pattern in which boundary portions are continuously connected is formed. By utilizing this principle, it becomes possible to create a printed matter having a natural fluctuation and having a repeating pattern.

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below with reference to illustrated embodiments.

§1. One-Dimensional Fractal Lattice The basic idea of the present invention is to reflect the natural fluctuation expressed by the fractal lattice in the pattern of the printed matter. Therefore, first, a brief description of this fractal lattice will be given. Here, the one-dimensional fractal lattice will be described with reference to the drawings.

Now, as shown in FIG. 1, two grid points A and B (indicated by double circles in the figure) are defined on one line at a predetermined distance, and these grid points A and B are defined. Scalar values a and b are defined in B, respectively. The two grid points A and B defined in this way are in the initial stage (hereinafter called the 0th stage).
, And the scalar values a and b are, so to speak, initial conditions set to these two grid points A and B.

Subsequently, as shown in FIG. 2, the grid point C of the first stage is defined at the midpoint between the two grid points A and B. At this time, a scalar value c is also defined for this lattice point C, but this scalar value c is a scalar value a, b.
, And is defined by a predetermined calculation.
FIG. 2 shows a state in which the scalar value c of the grid point C has not yet been determined. It should be noted that here, the lattice points in the state where the scalar value is undefined are indicated by a single circle, and the lattice points in the state where the scalar value is defined are indicated by a double circle. The scalar value c is calculated by the following arithmetic expression c = (a + b) /2+T.RND (1). Here, a and b are grid points A
And B are scalar values defined for B, T is the maximum half-amplitude value of the fluctuation, and RND is an arbitrary random number such that −1 ≦ RND ≦ + 1. As described above, a random number is used to define the scalar value c, and an accidental element affects it. However, as the scalar value c, a completely random value is not defined, and the grid points A and B on both sides are not defined.
Will be limited by the scalar values a and b of and the maximum half amplitude value T. That is, as shown in the above equation (1), the average value of the scalar values a and b is -T ~
The value obtained by adding an arbitrary value (determined by a random number) within the range of + T becomes the value of the scalar value c. Therefore, the maximum half-amplitude value T is a parameter that limits the degree of fluctuation that deviates from the average value.

In this way, if the scalar value c for the grid point C in the first stage can be defined, then, as shown in FIG. ,
Second-stage grid points D and E are defined respectively. And
For these grid points D and E, scalar values d and
e is calculated by the following equation: d = (a + c) / 2 + (1/2) .T.RND (2) e = (c + b) / 2 + (1/2) .T.RND (3) Here, as described above, T
Is the maximum half-amplitude value of fluctuation, and RND is −1 ≦ RND ≦ +
It is an arbitrary random number of 1. It should be noted that the expressions (2) and (3) are very similar to the expression (1), but that the maximum half amplitude value T is multiplied by a coefficient of (1/2).

Subsequently, a grid point of the third stage is defined at each of the midpoints of the five grid points A, D, C, E and B defined up to the second stage, and the grid points are also scalar. Calculate and define the value. For example, the scalar value f for the grid point F (not shown) defined as the midpoint of the grid points A and D is: f = (a + d) / 2 + (1/4) .T.RND (4) It is calculated by the formula. In this equation (4), the maximum half amplitude value T is multiplied by a factor of (1/4).

To facilitate understanding, the above steps will be described using actual numerical values. For example, as shown in FIG. 4, consider a case where scalar values “50” and “80” are set as initial conditions for the 0th stage grid points A and B, respectively. As shown in FIG. 5, the grid point C of the first stage is defined as the midpoint between the two grid points A and B. In this case, a scalar defined for this grid point C is used. The value c is given by the equation: c = (50 + 80) /2+T.RND (1) according to the equation (1). Here, the maximum half-amplitude value T of the fluctuation is set to 5 and the random number R happens to be R when the above equation is calculated.
Let's assume that ND = + 0.6. In this case, the scalar value c = 68 calculated.

Subsequently, grid points A and C and grid points C and B
As the middle point, as shown in FIG. 6, the grid point D of the second stage
And the grid point E will be defined. In this case,
The scalar values d and e defined for these lattice points D and E are calculated by the above equations (2) and (3) as follows: d = (50 + 68) / 2 + (1/2) .T.RND (2) e = (68 + 80) / 2 + (1/2) .T.RND (3) Here, if it is assumed that the random numbers RND = -0.4 and RND = + 0.8 happen to occur during the calculation of the above equations, the scalar value d = 5 obtained by the calculation.
8, e = 76. After all, at the stage where the scalar value about the grid point of the second stage is obtained, as shown in FIG.
Scalar values are defined for the five grid points A, D, C, E, and B, respectively.

Similarly, these five grid points A,
At each of the midpoints of D, C, E, and B, grid points of the third stage are defined, and scalar values are calculated and defined at these grid points, and further, the fourth, fifth, ... Repeat the same operation as. This operation is performed a predetermined finite number of times n
If this is repeated, a large number of grid points are defined between the grid points A and B of the 0th stage, and a predetermined scalar value is defined at each of these grid points. In addition, if the calculation method of the scalar value s about the lattice point of the nth stage is shown by a general formula, it will become s = ((alpha) + (beta)) / 2+ (1/2 ^(n-1) ) * T * RND (5). Here, α and β are scalar values (calculated in the (n−1) th stage) of grid points on both sides of the grid point, and T is the maximum half-amplitude value of the fluctuation, as described above. RND is an arbitrary random number such that −1 ≦ RND ≦ + 1.

When a large number of grid points having a predetermined scalar value are defined by such a method, these grid points form a one-dimensional fractal grid. Such a fractal grid generation method is generally called a random midpoint displacement method. In the above-mentioned specific example, a scalar value of "50" is defined at the left end point and "80" at the right end point of this one-dimensional fractal grid, and a large number of grid points defined between these end points also A unique scalar value is defined. Now, when the horizontal axis represents the array direction of the one-dimensional fractal lattice obtained in this way and the vertical axis represents each scalar value, a graph as shown in FIG. 8 is drawn. Such a graph has, for example, a property similar to the shape of a natural coastline. That is, the individual scalar values have various distributions such as partially increasing or decreasing, but the complexity of this distribution pattern is microscopically or macroscopically viewed. It is known to be the same. To explain this property more specifically, the complexity of the graph between the grid points AB and the complexity of the graph between the grid points AD are the same in FIG.
In addition, when a very small section between the grid points AD is magnified with a magnifying glass, it also has the same complexity. In other words, the individual scalar values are self-similarly defined at the individual grid points, and are spatially increased or decreased with natural fluctuations.

§2. Two-dimensional fractal grid or more, a method of generating a simple one-dimensional fractal grid by the random midpoint displacement method has been described with a specific example, but the fractal grid actually used in the examples described later is a grid. It is a two-dimensional fractal grid in which points are arranged in a plane. Therefore, here, an example of a method in which the random midpoint displacement method described in the above-described one-dimensional fractal grid is applied to two-dimensional will be described. In order to generate a two-dimensional fractal lattice,
As shown in FIG. 9, the grid points A, B, and
C and D are arranged to define scalar values a, b, c and d, respectively. Here, this square is an outline rectangle forming the outline of the finally generated two-dimensional fractal lattice.

Then, as shown in FIG. 10, grid points AB
Grid points E, F, G, and H of the first stage are defined at the midpoints of the grids, BCs, CDs, and DAs, respectively, and at the intersection of the diagonal lines of the four grid points ABCD, another first grid point is defined. Define a grid point I of a stage. Then, scalar values e, f, g, h, and i are defined for these five grid points, respectively, and this is calculated by the following equation e = (a + b) /2+T.RND (6) f = (B + c) /2+T.RND (7) g = (c + d) /2+T.RND (8) h = (d + a) /2+T.RND (9) i = (a + b + c + d ) /4+T.RND (10). As in the example of the one-dimensional fractal lattice, T is the maximum half-amplitude value of fluctuation and RND is −1.
It is an arbitrary random number such that ≦ RND ≦ + 1.

Thus, the grid points E, F, G of the first stage are
Once the scalar values e, f, g, h, i for H and I have been defined, subsequently, as shown in FIG. 11, at the midpoint of each adjacent grid point and the intersection of the diagonals of the four grid points, The grid points J, K, L, M, N, ... of the second stage are defined respectively (in order to avoid complication, only grid points J, K, L, M, N are displayed with grid point names in FIG. 11). Have been done). Then, for each of these lattice points, scalar values j, k, l, m, n, ... Are defined, respectively. This is the following arithmetic expression (only the arithmetic expressions for j to n are shown) j = (A + e) / 2 + (1/2) .T.RND (11) k = (e + i) / 2 + (1/2) .T.RND (12) l = (i + h) / 2 + (1 / 2) · T · RND (13) m = (h + a) / 2 + (1/2) · T · RND (14) n = (a + e + i + h) / 4 + (1/2) · T -Calculate by RND (15). In the equation for obtaining the scalar value of the grid point at the second stage, the maximum half amplitude value T is multiplied by a coefficient of (1/2), as in the case of the one-dimensional fractal grid described above.

Similarly, the third stage, the fourth stage, ...
If the process of the nth stage is repeatedly executed, the scalar value will be defined for a large number of grid points arranged on the two-dimensional plane.

The above process will be described as a general theory.
First, in the 0th stage, four grid points are defined at the four corner positions of the outer shape rectangle, and predetermined scalar values are defined at each grid point. Then, as the processing of the i-th stage, the following processing may be sequentially executed. That is, first, the minimum rectangle at the current stage that does not include the grid points defined up to the (i-1) th stage is recognized. For example, in the case of the first stage where i = 1, the rectangle ABC shown in FIG.
D is the minimum rectangle (the grid points A defined up to the 0th stage,
B, C, and D are not included inside), and in the case of the second stage of i = 2, four rectangles AEIH and E shown in FIG.
BFI, HIGD, and IFCG are the smallest rectangles (first
It is a rectangle that does not include any of the grid points A to I defined up to the stage.

Then, grid points to be defined in the i-th stage are generated at the midpoints of the sides of the minimum rectangle and the center point of the minimum rectangle (for example, in the case of the first stage where i = 1, As shown in FIG. 10, the midpoint E of each side of the minimum rectangle ABCD,
Lattice points to be defined are generated at F, G, H and center point I). Furthermore, of these grid points, the grid point generated at the midpoint of each side has the scalar value of the two grid points defined up to the (i-1) th stage existing at the end points of the side. Gives a scalar value obtained by operating a random number. For example, the grid point E shown in FIG.
, The scalar value a of two grid points A and B,
The scalar value e obtained by applying the random number RND to b is given. In general, if the calculation method of the scalar value s1 for the grid point defined as the midpoint of the adjacent grid points in the n-th stage is shown by an equation, then s1 = (α + β) / 2 + (1/2 ^(n-1) )・ T ・ RND (16). Here, α and β are scalar values (calculated in the (n−1) th stage) of the grid points on both sides of the grid point.

On the other hand, the grid points generated at the center point of the minimum rectangle are located at the four corners of the minimum rectangle (i
-1) Give a scalar value obtained by applying a random number to the scalar values of the four grid points defined up to the step. For example, for the grid point I shown in FIG. 10, the scalar value a, which four grid points A, B, C, D have,
A scalar value i obtained by applying a random number RND to b, c, and d is given. Generally, if the calculation method of the scalar value s2 for the lattice point defined as the center point of the minimum rectangle in the nth stage is shown by an equation, s2 = (α + β + γ + δ) / 4 + (1/2 ^(n-1) ). It becomes T.RND (17). Here, α, β, γ, δ are 4 of the smallest rectangle.
It is a scalar value of a grid point at one corner (calculated in the (n-1) th stage).

The two-dimensional fractal lattice generated by such a method eventually gives a scalar field spread in a two-dimensional plane. Therefore, if the surface of this two-dimensional fractal grid is placed on a horizontal plane and each scalar value is plotted as a height (elevation) in the vertical direction on a graph, a concavo-convex pattern such as a mountain ridge structure can be expressed. It is known that such a raised structure has properties similar to the uneven pattern of the actual mountain raised structure existing in nature.
That is, the complexity of the concavo-convex structure is the same from a microscopic point of view and a macroscopic point of view, and the magnifying glass magnifying part of the concavo-convex structure has the same complexity. In other words, the individual scalar values distributed on the two-dimensional plane are arranged in a self-similar manner, and spatially increase or decrease with natural fluctuations.

§3. Repeatable Unit Fractal Lattice Now, assume that the two-dimensional unit fractal lattice 10 as shown in FIG. 12 is generated by the random midpoint displacement method described above. This two-dimensional unit fractal grid 10 has a large number of grid points 11 arranged vertically and horizontally (here, 1 for convenience.
Each grid point 11 is defined with a predetermined scalar value. In other words, the two-dimensional unit fractal grid 10 can be considered as a square board in which a large number of tiles each having a predetermined number are arranged in a matrix.

Then, as shown in FIG. 13, by arranging nine such square boards on a plane, a board having an area nine times larger can be obtained. Here, the large fractal lattice thus obtained will be referred to as a two-dimensional synthetic fractal lattice 20. The word "unit" in the two-dimensional unit fractal lattice 10 shown in FIG. 12 is used in correspondence with the word "synthesis" in the "two-dimensional synthetic fractal lattice 20" shown in FIG.

By the way, the two-dimensional unit fractal lattice 10
The scalar field defined in gives a natural fluctuation as far as it is within this closed region of the unit cell. However, the scalar field defined in the two-dimensional synthetic fractal lattice 20 as shown in FIG. 13 does not always give a natural fluctuation as a whole. This is because the boundary portions shown by hatching in FIG. 13 are not continuously connected. In other words, at this boundary, the scalar field becomes discontinuous and the natural fluctuation is disturbed. In the present invention, as a whole, a "unit fractal lattice" that can obtain a scalar field that gives natural fluctuations is referred to as a "repeatable unit fractal lattice" even when a plurality of them are spatially adjacent to each other. I will call it. Therefore, if the two-dimensional unit fractal lattice 10 shown in FIG. 12 is a “repeatable unit fractal lattice”, the two-dimensional synthetic fractal lattice 20 shown in FIG. 13 can provide a scalar field that gives a natural fluctuation as a whole. .

Next, the basic concept for generating a repeatable two-dimensional unit fractal lattice will be described with reference to FIG. Now, let us consider a two-dimensional unit fractal lattice 30 in which an outer rectangle which is the outer shape of the lattice is constituted by four sides of a left side 31, a right side 32, an upper side 33, and a lower side 34, as shown in FIG. 14 (a). At this time, as a scalar value given to an arbitrary grid point 35 on the grid row along the lower side 34 hatched in the figure, the upper side 33 also hatched in the figure is shown.
If the same value as the scalar value given to the grid point 36 located at the same lateral position on the grid row along is given, if this unit fractal grid is arranged in multiple rows, the scalar field at the boundary will be continuous. Become. Similarly, in FIG. 14 (b), as a scalar value given to an arbitrary grid point 37 on the grid row along the right side 32 hatched in the figure, the grid row along the left side 31 also hatched in the figure is shown. When the same value as the scalar value given to the grid point 38 at the same vertical position is given, the scalar field at the boundary becomes continuous when a plurality of unit fractal grids are arranged on the left and right. After all, as the scalar value of the grid point 35 on the lower side 34, the scalar value of the grid point 36 on the upper side 33 is diverted, and as the scalar value of the grid point 37 on the right side 32, the scalar value of the grid point 38 on the left side 31 is used. If you use the scalar value,
Scalar values of grid points at the boundary portion hatched at 3 are continuous.

The basic concept of the present invention for generating a repeatable two-dimensional unit fractal grid is as described above.
This is a method of diverting the scalar value of the grid point on the opposite side of the outer rectangle. However, when the already generated two-dimensional unit fractal grid is modified by diverting the scalar value as described above, the grid point on the outer rectangle and the grid point immediately inside the grid point become discontinuous. turn into. Therefore, in the present invention, a method of diversion of this scalar value is incorporated in the fractal lattice generation process, and while maintaining a continuous scalar field inside the unit fractal lattice, a continuous scalar field is realized even at the boundary portion. I am able to do it. Hereinafter, a method for generating this repeatable two-dimensional unit fractal lattice will be described with reference to a specific example.

§4. Repeatable 2D unit fractor
Method of generating le lattices To generate a repeatable two-dimensional fractal lattice,
As shown in FIG. 15, grid points A, B, C, and D are arranged at the four vertexes of the outer shape rectangle as the grid points at the 0th stage, and the same scalar value a is defined at each grid point.

Subsequently, in the first stage, as shown in FIG. 16, grid points E, F, G, and H are defined at midpoints between grid points AB, BC, CD, DA. , The smallest rectangle at this point (the same rectangle ABCD as the outer rectangle)
Define another grid point I at the center point of. Scalar values e, f, g, h, and i are defined for these five grid points, respectively. The scalar value f for the grid point F on the right side of the outer shape rectangle and the grid point on the lower side of the outer shape rectangle are defined. When determining the scalar value g and G for G, a method peculiar to the present invention, which is the diversion of the scalar value described in §3, is adopted, instead of the usual method for calculating the scalar value described in §2. . That is, if this is expressed by an arithmetic expression, e = (a + a) /2+T.RND (18) h = (a + a) /2+T.RND (19) i = (a + a + a + a) / 4 + T · RND (20) f = h (21) g = e (22). Where T is the maximum half-amplitude value of fluctuation, RND
Is an arbitrary random number such that −1 ≦ RND ≦ + 1. As a result, exactly the same scalar value is defined for each corresponding grid point on the left and right sides of the outer shape rectangle ABCD, and exactly the same scalar value is defined for each corresponding grid point on the upper and lower sides. become.

Thus, the grid points E, F, G, of the first stage are
Once the scalar values e, f, g, h, i for H and I have been defined, the process then proceeds to the second stage, as shown in FIG. 17, where the four smallest rectangles AEIH, EBFI, IFCG,
After recognizing the HIGD, new grid points J to Y are generated at the respective midpoint positions and center points of the four sides for each minimum rectangle. Then, the scalar values j to y are defined at the respective grid points J to Y. In this case, basically, the scalar value defined for each grid point is calculated according to the calculation method described in §2, except that the scalar value for the grid point on the right side of the outer rectangle is the corresponding position on the left side. The scalar value for the grid point of is diverted, and the scalar value for the grid point on the lower side of the outer shape rectangle is diverted for the grid point at the corresponding position on the upper side. Specifically, in FIG. 17, for new grid points N and O defined on the right side of the outer shape rectangle ABCD and new grid points P and Q defined on the lower side, scalar values calculated by normal operation are used. Instead, a scalar value will be given by diversion. That is, this external rectangle ABC
Scalar values j to q given to eight newly defined lattice points J to Q on D are j = (a + e) / 2 + (1/2) .T.RND (23) k = (e + a) / 2 + (1/2) ・ T ・ RND (24) l = (a + h) / 2 + (1/2) ・ T ・ RND (25) m = (h + a) / 2 + (1/2) ・ T ・RND (26) n = 1 (27) o = m (28) p = k (29) q = j (30). Here, a scalar value for a new grid point J, K defined on the upper side of the outer shape rectangle ABCD and a scalar value j for a new grid point L, M defined on the left side of the outer shape rectangle ABCD.
The arithmetic expressions (23) to (26) for obtaining ~ m are the ordinary arithmetic expressions described in §2, but for the new grid points N and O defined on the right side of the outline rectangle ABCD. Equations (27) to (30) for obtaining the scalar values n to q of the new lattice points P and Q defined on the lower side of the outline rectangle ABCD are simply the scalar values of the corresponding lattice points. It shows the diversion of. In addition, the scalar values r to y given to the eight newly defined grid points R to Y inside the outline rectangle ABCD are the normal arithmetic expressions described in §2, r = (a + e + i + h) / 4 + (1/2) ・ T ・ RND (31) s = (e + i) / 2 + (1/2) ・ T ・ RND (32) t = (e + a + f + i) / 4 + ( 1/2) ・ T ・ RND (33) u = (f + i) / 2 + (1/2) ・ T ・ RND (34) v = (i + f + a + g) / 4 + (1/2)・ T ・ RND (35) w = (g + i) / 2 + (1/2) ・ T ・ RND (36) x = (h + i + g + a) / 4 + (1/2) ・ T ・ RND (37) y = (h + i) / 2 + (1/2) .T.RND Calculated by (38).

After all, as shown in FIG. 17, of the 25 grid points A to Y defined up to the second stage, the outer shape rectangle A is used.
The scalar values of the grid points B, N, F, O, and C on the right side of the BCD are the same as the scalar values of the grid points A, L, H, M, and D on the left side, respectively.
The scalar values of the grid points D, Q, G, P, C on the lower side of CD are the same as the scalar values of the grid points A, J, E, K, B on the upper side, respectively. Since the processing from the third stage onward is performed in exactly the same manner, a repeatable two-dimensional unit fractal lattice is finally obtained. That is, as shown in FIG. 13, when a plurality of elements are arranged in a plane, the boundary portions are continuously connected. In addition, since the diversion processing of the scalar values for the grid points on the right side and the grid points on the lower side of the outer shape rectangle is performed for each process of each step of generating the fractal grid, the finally generated fractal grid is It becomes natural with a continuous scalar field inside.

By the way, the method of arranging the two-dimensional unit fractal lattice on a plane without a gap is not limited to the method shown in FIG. For example, as shown in FIG. 18, there is also a method of arranging the upper and lower rows by shifting them by the offset amount W in the horizontal direction. In this way, in the case of generating a repeatable two-dimensional unit fractal grid, which is assumed to be arranged with a shift amount of W,
It is not always possible to use the grid points at the same position on opposite sides of the outer rectangle as they are as the other party to whom the scalar value is diverted. This can be easily understood by considering the positional relationship of various geometric symbols shown in the boundary portion in FIG. This concept is shown in FIG. As shown in FIG. 19 (a), for the grid point 12 on the right side, the scalar value of the grid point 13 at the same position on the left side can be diverted as it is as in the above example, but on the bottom side. Grid point 1
For 4, it is necessary to consider the grid point 15 at a position shifted by the offset amount W and to use the scalar value of the grid point 16 at the same position as the grid point 15 on the upper side. Further, as shown in FIG. 19B, when the grid point 17 on the lower side is offset from the unit grid by shifting it by the offset amount W to the left, the remaining offset amount is shifted from the right end of the unit grid. Considering the grid point 18 at the position, it is necessary to divert the scalar value of the grid point 19 at the same position as the grid point 18 on the upper side.

In the above example, the offset direction is the horizontal direction, but the offset direction can be the vertical direction. However, in any case, if the offset amount is determined, the connection corresponding position on the upper side with respect to the predetermined position on the lower side and the connection corresponding position on the left side with respect to the predetermined position on the right side are uniquely obtained. Therefore, if the scalar values for the grid points at the corresponding connection positions are diverted, no matter what array is used,
It is possible to generate a repeatable two-dimensional unit fractal grid.

§5. Repeatable 2D unit fractor
Generating Procedure of Leu Lattice Here, a general procedure for generating a repeatable two-dimensional unit fractal lattice will be described based on the flowchart of FIG. First, in step S1, the lattice size n and the maximum half amplitude value T are set. Here, the lattice size n is the resolution of the generated fractal lattice, that is,
This shows the lattice density, and in this example, the lattice size is defined by the number of stages n indicating how many stages the above-mentioned work of generating lattice points is performed (if n = 1, as shown in FIG. 16). If the size is 3 × 3 and n = 2, a fractal lattice of size 5 × 5 is generated as shown in FIG.

Next, in step S2, a parameter i indicating the number of stages being processed is set to an initial value 0. That is, the process of the 0th stage is performed from now on, and thereafter, the respective processes described below are repeatedly executed until the parameter i is sequentially increased by 1, 2, 3, ... Until i = n. It will be.

Step S3 shows the process of the 0th stage. That is, in the 0th stage, as shown in FIG. 15, four grid points A, B, C, D are provided at four corner positions of the outer shape rectangle.
Is defined, and a common scalar value a is given to these grid points. Note that this scalar value a and step S1
The maximum half-amplitude value T set in step 1 becomes a factor that determines the absolute value of the scalar value and the fluctuation width of the finally obtained fractal grid. Therefore, in the image generation processing described later, the values of a and T may be appropriately set in consideration of the absolute value and the fluctuation width of the scalar field.

In the next step S4, the parameter i
Is incremented by 1. As a result, the initial stage of i = 0 shifts to the first stage of i = 1, and the process of the first stage is performed thereafter.

Step S5 is the first process in each stage and is the process of generating grid points in the i-th stage.
A general definition of this processing is as follows. First, the minimum rectangle at the current stage that does not internally include the grid points defined up to the (i-1) th stage is recognized. In the case of the first stage of i = 1, the rectangle ABCD shown in FIG. 9 is recognized as the minimum rectangle that does not include the grid points A, B, C, D defined up to the 0th stage. Also,
In the case of the second stage of i = 2, the grid points A to I defined up to the first stage are set as the minimum rectangles that are not included in the inside of FIG.
4 rectangles AEIH, EBFI, IFCG, HI shown in
GD is recognized. Then, five new grid points are generated for each recognized minimum rectangle (the grid points generated for the adjacent minimum rectangles are partially overlapped). In particular,
New grid points are generated at the midpoint position of each of the four sides of the minimum rectangle and the center point position of the minimum rectangle.

In the following step S6, a scalar value is defined for the new grid point generated in step S5, using the maximum half amplitude value T set in step S1 and the random number RND. At this time, as a general rule, for the grid point generated at the midpoint of each side of the minimum rectangle, s1 = (α + β) / 2 + (1/2 ^(i-1) ) · T · RND (16) Using the scalar value s1 obtained by the above, for the grid point generated at the center point of the minimum rectangle, s2 = (α + β + γ + δ) / 4 + (1/2 ^(i-1) ) T RND (17) The scalar value s2 obtained by is used. However, as an exception, for the grid point on the right side of the outer rectangle, the scalar value of the grid point at the connection corresponding position on the left side is diverted, and for the grid point on the lower side, the scalar value of the grid point at the connection corresponding position on the upper side is used. Transfer scalar value.

Then, in step S7, whether or not the set grid size is obtained, that is, the parameter i
= N is determined, and if i <n, the processing from step S4 is repeatedly executed again. In this way, when the processing up to the nth stage is executed, the desired repeatable two-dimensional unit fractal lattice is completed.

In the above description, for the grid point on the right side of the outer rectangle, the scalar value of the grid point at the connection corresponding position on the left side is diverted, and for the grid point on the lower side,
The scalar value of the grid point at the connection corresponding position on the upper side is diverted, but conversely, for the grid point on the left side of the outer shape rectangle, the scalar value of the grid point at the connection corresponding position on the right side is diverted. Alternatively, for the grid point on the upper side, the scalar value of the grid point at the connection corresponding position on the lower side may be diverted.

Further, the method of generating a repeatable two-dimensional fractal grid by using the random midpoint displacement method has been described so far, but this method can generate a one-dimensional fractal grid or a three-dimensional or more fractal grid. It can be used similarly when generating. For example, in order to generate a repeatable one-dimensional fractal grid, it is sufficient to set the same scalar value to two grid points in the 0th stage. In order to generate a repeatable three-dimensional fractal grid, grid points having the same scalar value are defined at the eight corners of the cube at the 0th stage, and grid points on the three faces of this cube are defined as follows. The scalar value of the lattice point on each facing surface may be diverted. For example, even if this cube is used as a dice, for the lattice points on the face of the 1st eye, the scalar value of the lattice point on the face of the 6th eye is diverted, and 2
For the grid points on the face of the eye, the scalar value of the grid point on the face of the fifth eye is diverted, and for the grid point on the face of the third eye, scalar of the grid point on the face of the fourth eye The value should be diverted.

§6. Image Creating Apparatus According to the Present Invention So far, a method for generating a repeatable unit fractal grid has been described. This repeatable unit fractal lattice is an important concept related to the essence of the present invention, but the substance of the present invention is to use the repeatable unit fractal lattice to create an image having a repeating pattern.
Is in the device that produces . Therefore, in FIG. 21, according to the present invention,
FIG. 1 is a block diagram showing the basic configuration of an apparatus that creates a printed image and further creates a printed matter .

This apparatus has a fractal condition setting unit 1 for setting conditions necessary for generating a unit fractal grid.
, A random number generator 2 for generating random numbers for giving fluctuations to the scalar value given to each lattice point constituting this unit fractal lattice, the conditions set in the fractal condition setting unit 1, and the random number generator 2 When a plurality of generated unit fractal grids are spatially arranged, a scalar value calculation unit 3 that calculates a scalar value to be given to each grid point by a predetermined calculation based on the generated random numbers is used. So that the boundary parts of are continuously connected,
Scalar value diversion unit 4 that diverts a scalar value to be given to a predetermined grid point at the boundary from a scalar value at another grid point.
And a scalar value calculated by the scalar value calculation unit 3 or a scalar value converted by the scalar value conversion unit 4 to each grid point to generate a repeatable unit fractal grid fractal grid generation unit 5 A pattern condition setting unit 6 for setting conditions necessary to generate a unit pattern expressed as a printed matter; each scalar value distributed in the repeatable unit fractal grid generated by the fractal grid generation unit 5; A unit image composed of pixels distributed in a predetermined unit area is generated by a predetermined operation based on the condition set in the condition setting unit 6, and a plurality of unit images are spatially arranged to spatially An image generation unit 7 that generates a composite image in which a repeating pattern is expressed, and a composite image generated by this image generation unit 7 are printed. An image printing section 8 forming the Butsujo are constituted by.

Here, the fractal condition setting unit 1 has the size n of the unit fractal grid to be generated, the maximum half-amplitude value T, and the same position arranged at each of the four corners of the outer shape rectangle forming the outer shape of the grid. An initial grid point with a scalar value a of
20 is set as a condition, and also has a function of setting steps S1 and S3 in the flowchart shown in FIG. Further, the random number generator 2 has a function of generating a random number RND in the range of −1 ≦ RND ≦ + 1 in the case of the embodiments described so far. Further, the scalar value calculation unit 3 executes step S6 in the flowchart shown in FIG.
20. The scalar value diversion unit 4 has the function of performing the basic scalar value calculation process shown in FIG. 20, and the scalar value diversion unit 4 has the function of performing the exceptional scalar value diversion process at step S6 in the flowchart shown in FIG. The fractal grid generation unit 5 defines new grid points at the center points of the midpoints of two adjacent grid points and the four grid points forming the minimum rectangle, and in principle, a scalar value calculation is performed on each of these grid points. The calculated scalar value obtained by the section 3 is given. However, when each of these grid points is a grid point on the right side or the lower side of the outer rectangle, the diversion scalar value calculated by the scalar value diversion section 4 is exceptionally set. Perform the process of giving.

As described above, the fractal grid generating section 5 generates a repeatable unit fractal grid in this manner. The image generation unit 7 uses the self-similar scalar field distributed in the repeatable unit fractal lattice in a specific method based on the predetermined condition set in the pattern condition setting unit 6 (for this specific method, , Which will be described later), and a predetermined unit image is generated. As a result, a pattern with natural fluctuations based on a self-similar scalar field is formed in this unit image, and this pattern has continuous boundary parts when a plurality of patterns are arranged on a plane. It becomes a pattern that is connected. Therefore, the image generation unit 7 generates a composite image by arranging a plurality of such unit images. This composite image is composed of continuous patterns with natural fluctuations as a whole. Therefore, if the image printing section 8 prints this composite image on a wallpaper or the like, it becomes possible to create a wallpaper having a repeating pattern with natural fluctuations.

Of the constituent elements shown as blocks in FIG. 21, the image printing unit 8 is an element configured by a machine such as an actual printing machine, but the other constituent elements are all realized by a computer. Each block represents individual processing performed by this computer as a functional block. Of these functional blocks, the processing contents of the blocks that contribute to the generation of the repeatable unit fractal lattice are believed to have been fully understood by the above description. Therefore, the setting contents of the pattern condition setting unit 6 and the processing contents of the image generating unit 7 will be described in detail below.

The image generation processing by the image generation unit 7 is
It suffices if the self-similar scalar field distributed in the repeatable unit fractal lattice is used in some form and the natural fluctuation due to this scalar field is captured in the unit image. In this specification, 3 of such processes
One specific example will be disclosed separately in §7 to §9.

§7. Determine pixel value based on scalar value
The easiest way to produce a single image using a self-similar scalar field distributed in methods repeatable unit fractal grating constant is a method for determining a pixel value based on the scalar value. In this method, an equation for converting a scalar value into a pixel value may be prepared in the pattern condition setting unit 6. For example, when the simplest conversion formula with scalar value = pixel value is prepared in the pattern condition setting unit 6, the image generation unit 7
Will generate a unit image in which each grid point of the repeatable two-dimensional unit fractal grid provided from the fractal grid generation unit 5 is used as each pixel as it is. In this case, for each pixel of the unit image, the scalar value of the corresponding lattice point is directly given as the pixel value.
When a repeatable two-dimensional unit fractal grid having a size of 5 × 5 as shown in FIG. 17 is prepared, a scalar value a to y given to each grid point is used as a pixel value, and a size of 5 × 5. Unit image is generated (though such a unit image having a size of about 5 × 5 is not realistic, and in practice, a larger size fractal grid is used to generate a larger unit image). Image is generated).

However, when printing is performed in the image printing unit 8, it is general that a range of pixel values is limited (for example, when one pixel is represented by 8 bits, A value within the range of 0 to 255 is required). In addition, the range of pixel values may be limited due to the requirements of actual products such as wallpaper (for example,
To print a bright wallpaper, set the pixel value to 200-255
Limit to). In such a case, in the pattern condition setting unit 6, in order to obtain a pixel value within a predetermined range,
A predetermined conversion formula for converting the scalar value in the unit fractal grid into the pixel value in the unit image may be prepared.

Further, if the correspondence between each pixel and each lattice point is defined in the pattern condition setting unit 6, it is possible to generate a unit image having a size different from the prepared unit fractal lattice. For example, when a unit image with a size of n × n is generated (when a reduced unit image is generated) based on a unit fractal grid with a size of 2n × 2n, each pixel in the unit image is converted into a unit fractal. It suffices to define a correspondence relationship that associates with every other grid point in the grid. On the contrary, when a unit image having a size of 2n × 2n is generated based on a unit fractal grid having a size of n × n (when an enlarged unit image is generated), 1 in the unit image is generated.
Correspondences are defined such that every third pixel is associated with each grid point in the unit fractal grid, and for pixels without corresponding grid points, the average value of the pixel values of adjacent pixels is used as the pixel value. You can also give it.

In any case, the unit image thus generated becomes repeatable as in the original unit fractal grid. Therefore, in the image generation unit 7,
If a composite image is generated by arranging a large number of unit images on a plane, a pattern having fluctuation based on a fractal lattice will be expressed in the composite image, and this pattern will also appear in the unit image. It seems that continuous connection is made at the boundary.

§8. Original image based on scalar value
In the method explained in §7 above, since the scalar value in the unit fractal grid is reflected as it is as the pixel value, the created pattern as a whole has a shading distribution with natural fluctuation. It becomes a pattern expressed by. Therefore, for example, it is not possible to create an intentional pattern such as a striped pattern, a polka dot pattern, a wood pattern, a stone pattern.
The method described here uses the scalar value in the unit fractal grid as the displacement amount, and the original image (intentional pattern)
Is a method of generating a unit image by distorting.

The above-mentioned striped pattern, polka dot pattern, wood grain pattern,
An intentional pattern such as a stone pattern can be artificially created easily by using a computer graphics technique. For example, as shown in FIG.
Geometric concentric cylinder 4 in XYZ three-dimensional coordinate system
Considering the cross-sectional pattern when a model of 0 is cut and cut on the XY plane 50, as shown in FIG.
It can be seen that the annual ring pattern 51 is obtained above. In place of the simple concentric cylinder 40, if a simulated tree model that more accurately simulates the shape of the tree and the density distribution inside the tree is created, it is possible to obtain a grain pattern closer to natural eyes on the plane 50. Become. Further, if the plane 50 is inclined (generally, in the case of wallpaper patterns, etc.), or if a curved surface is used instead of the plane 50, a more varied pattern can be obtained. in this way,
Various methods are known for artificially creating a wood grain pattern by computer simulation, and by appropriately setting the simulation conditions,
It is also possible to obtain a repeatable pattern (a pattern in which boundary portions are continuously connected when a plurality of patterns are arranged on a plane).

However, the pattern created by the artificial simulation as described above, when observed with human eyes,
It gives an unnatural impression. The inventor of the present application considers that the reason why such an unnatural impression is given is that the artificially generated pattern does not include a natural fluctuation component. Therefore, we tried to distort the image with such artificially generated pattern as the displacement value of the scalar value in the unit fractal grid, and confirmed that it could be converted into an image with a more natural impression. It was The image conversion method will be described below.

First, the image data of the unit image P to be converted as shown in the upper part of FIG. 24 is prepared. This unit image P has coordinate positions (x,
23), an image formed by arranging a pixel P (x, y) having a predetermined pixel value in y).
An image including some artificially created pattern, such as the annual ring pattern 51 shown in FIG. Moreover, this pattern is assumed to be a repeatable pattern. The purpose of the image conversion processing to be performed from now on is to obtain a unit image Q as shown in the middle part of FIG. 24 based on such a unit image P. Here, like the unit image P, the unit image Q is configured by arranging a pixel Q (x, y) having a predetermined pixel value at a coordinate position (x, y) on the XY two-dimensional plane. It is assumed that both unit images P and Q have pixel arrays of the same size. The following process is a process of determining a pixel value for each pixel Q (x, y).

First, a repeatable two-dimensional unit fractal lattice F as shown in the lower part of FIG. 24 is prepared. The array of grid points forming this repeatable two-dimensional unit fractal grid F does not necessarily have to be the same size as the pixel array of the unit images P and Q, but for any one pixel in the unit image Q. Since it is necessary to associate one grid point at a spatially corresponding position, it is convenient to make the pixel arrays of the unit images P and Q and the grid point array of the fractal grid F the same size. is there. That is, if the arrays of the same size are used, one pixel in the unit image P, one pixel in the unit image Q, and
One lattice point in the fractal lattice F is simply associated with each other.

As described above, a predetermined scalar value having a self-similar property is defined at each lattice point forming the repeatable two-dimensional unit fractal F. Already §5
As described with reference to the flow chart in the above, such a repeatable two-dimensional unit fractal F can be generated by calculation by a computer. In this case, the exact value of the scalar value defined at each grid point cannot be controlled because random numbers are involved, but the overall rough value can be set to some extent. That is, in the case of the method described in §5, by setting the same scalar value a and the maximum half-amplitude value T of fluctuation given to the grid points A, B, C, and D at the 0th stage, the rough value of the scalar value is set. It is possible to set a rough increase / decrease range.
Therefore, considering that the scalar value S defined by the fractal grid F is used as the displacement amount d, it is necessary to generate the fractal grid F having the scalar value S suitable for use as the displacement amount d. preferable. For example, if this image conversion causes a distortion of about 10 pixels at the maximum, if the fractal grid F in which the scalar value S in the range of -10 to +10 is defined is generated and used, this scalar value S Can be used as is as the displacement amount d. However, if a value obtained by performing some calculation on the scalar value S is used as the displacement amount d, a fractal grid having any scalar value distribution may be prepared. For example, +90 to +11
Even when the fractal grid F in which the scalar value S in the range of about 0 is defined is used, if the displacement amount d = S−100, the displacement amount d distributed in the range of about −10 to +10.
Is obtained.

Now, the coordinate position (x, y) in the unit image Q
The pixel value Z to be given to the pixel Q (x, y) arranged at is can be determined by the following processing. First, the scalar value S defined for the grid point F (x, y) arranged at the same coordinate position (x, y) is recognized, and the displacement amount d is determined based on this scalar value S. As mentioned above,
If a predetermined relational expression is defined between the displacement amount d and the scalar value S, the displacement amount d suitable for causing the distortion can be obtained. Here, it is assumed that the displacement amount d = scalar value S and the scalar value S can be directly used as the displacement amount d. In this way, when the displacement amount d can be determined, the pixel P (x + d, y) arranged at the coordinate position (x + d, y)
Is specified as a reference pixel. This reference pixel P (x + d,
y) is a pixel displaced in the X direction by the displacement amount d with respect to the spatially corresponding pixel P (x, y) existing at the coordinate position (x, y). Then, the pixel value Z of the reference pixel P (x + d, y) is set as the pixel value to be given to the pixel Q (x, y). In addition, in the case where the displacement exceeds the contour line of the unit image P by shifting the displacement amount d, for example, when the contour line is exceeded, the unit image P moves to the opposite side, and a position displaced from the opposite side by the extra displacement amount. The pixel in is used as a reference pixel,
The predetermined method may be determined in advance.

When the pixel values are given to all the pixels forming the unit image Q by such a method, the conversion process from the unit image P to the unit image Q is completed. It should be noted that the above example is a process in which pixels are shifted in the X direction to distort an image in the X direction. When the image is distorted in the Y direction, the pixels may be shifted in the Y direction. That is, the pixel P (x, y + d) may be specified as the reference pixel.

As described above, the unit image P is distorted by using the scalar value in the fractal grid as the displacement amount, and the unit image Q is obtained as a result. The image Q thus obtained is obtained. Will contain a natural fluctuation component, and will appear as a more natural pattern to the human eye. Moreover, if an image having a repeatable pattern is prepared as the unit image P to be the base,
The unit image Q obtained by distorting this also becomes an image having a repeatable pattern. This can be easily understood by considering the conversion processing for the pixels on the boundary line.

For example, when the fractal grid F shown in the lower part is used to convert the unit image P shown in the upper part of FIG. 25 into the unit image Q shown in the middle part, the coordinate position of the upper side of the unit image Q is used. Pixel Q (a, b) existing in (a, b)
And the pixel Q (a, c) existing at the coordinate position (a, c) on the lower side
Consider what pixel value will be given for c) and. First, for the pixel Q (a, b) on the upper side, the scalar value S defined for the grid point F (a, b) arranged at the same coordinate position (a, b) is recognized, and this scalar value The displacement amount d is determined based on S.
On the other hand, for the pixel Q (a, c) on the lower side, the scalar value defined for the grid point F (a, c) arranged at the same coordinate position (a, c) is recognized, and this scalar value is determined. The displacement amount is determined based on the fractal grid F
Is a repeatable fractal grid, the grid point F
The same scalar value S is defined for (a, b) and the grid point F (a, c), and the displacement amount d also has the same value. Subsequently, using the displacement amount d, the pixel P (a + d, b) arranged at the coordinate position (a + d, b) in the unit image P.
Is determined as the reference pixel of the pixel Q (a, b), and the pixel P (a + d, c) arranged at the coordinate position (a + d, c) is determined as the reference pixel of the pixel Q (a, c). However, since the pair of reference pixels are at the same position (a + d) in the horizontal direction of the drawing, if the unit image P is an image having a repeatable pattern, the same pixel value Z (or,
Will have very close pixel values). After all, the pixel Q (a, b) on the upper side of the unit image Q and the pixel Q on the lower side
The same pixel value Z (or a pixel value that is very similar) is given to (a, c), and the unit image Q also becomes an image having a repeatable pattern. Therefore, when a plurality of obtained unit images Q are arranged on a plane to generate a composite image, a pattern having fluctuation based on a fractal lattice is expressed in the composite image, and moreover,
This pattern is a pattern in which continuous connection is made at the boundary portion of the unit images.

When the method described in this §8 is carried out by the device configuration shown in FIG. 21, the image data of the original unit image P and scalar value S A relational expression that determines the displacement amount d and a pattern condition may be set.

§9. Determine wrinkled surface based on scalar value
Meaning Method This method is a method of cutting a three-dimensional stereoscopic image at a predetermined plane and using the image appearing on the cut plane as a pattern.

For example, as shown in FIG. 26, a stereoscopic image of a geometrical concentric cylinder 45 is created in an XYZ three-dimensional coordinate system. At this time, it is assumed that pixels having different shades are defined in each part of the concentric cylinder 45 (in the example shown, gradation is applied concentrically like an annual ring of natural wood). Here, wrinkled surface 6
Prepare 0. The wrinkled surface 60 may be considered as a wrinkled surface obtained when, for example, a flat paper sheet is rolled into wrinkles and then flattened again. And
As shown in FIG. 26, the wrinkled surface 60 cuts the concentric cylinder body 45, and the pixels appearing on the cut surface are projected onto a predetermined projection surface 65. At this time, considering the pattern obtained on the projection plane 65, the annual ring pattern 61 having fluctuation as shown in FIG. 27 (the fluctuation component is not represented in the figure).
It can be seen that

Here, to define this wrinkled surface 60,
If the scalar field of the two-dimensional fractal lattice is used, the fluctuation of the annual ring pattern 61 becomes a self-similar natural fluctuation. Hereinafter, a method of defining the wrinkled surface 60 will be specifically described. For example, on a sheet of paper, 5 as shown in FIG.
A two-dimensional fractal grid having a size of × 5 is defined, and each grid point A to Y is displaced in a predetermined direction away from the original paper surface using the scalar values a to y as displacement amounts.
If both positive and negative values are prepared as scalar values, a certain grid point is displaced upward in the paper surface and a certain grid point is displaced downward in the paper surface. If a new surface is formed by the displaced lattice points, the new surface becomes wrinkled as a whole, and the wrinkled surface 60 is formed. However, with a size of 5 × 5, the wrinkled surface 60 obtained is a rather awkward surface, but in reality, a fractal grid of a larger size is used, and thus the wrinkled surface 60 thus obtained
Is a comparatively gentle surface with wrinkles due to the fluctuations of nature. As described above, when the concentric cylinder body 45 is cut by the wrinkled surface 60 in which wrinkles based on natural fluctuations are formed, the light and shade pattern expressed on the original concentric cylinder body 45 is artificial. Even so, the annual ring pattern 61 obtained on the projection surface 65 has a pattern with natural fluctuations.

It should be noted that cutting conditions are set such that a repeatable pattern is obtained on the projection surface 65 when cutting is performed on a wrinkle-free surface (for example, cutting by a surface perpendicular to the central axis of the concentric cylinder 45). By doing so, it is possible to obtain a repeatable pattern on the projection surface 65 even when the wrinkled surface 60 is used. To that end, a repeatable two-dimensional unit fractal grid may be used to define the wrinkled surface 60.
Therefore, the method shown in §9 can be sufficiently used practically for printed matter having a repeated pattern such as wallpaper.

In the above example, the image of the concentric cylinder 45 is used as the original three-dimensional stereoscopic image.
As the three-dimensional stereoscopic image, any stereoscopic image may be used as long as it is a stereoscopic image in which a large number of pixels having various pixel values are defined in the three-dimensional space. For example, even if a perfect geometric model such as a sphere whose pixel values are uniquely defined based on the distance from the center point is used, there is a natural fluctuation on the projection plane 65. A circular pattern will be obtained. When the method described in this §9 is implemented by the device configuration shown in FIG. 21, the original three-dimensional stereoscopic image data and the cutting condition are set as the pattern condition in the pattern condition setting unit 6. You can do it.

§10. Other Embodiments Although the present invention has been described based on the illustrated embodiments,
The present invention is not limited to these examples and can be implemented in various modes other than this. Some modifications will be described below.

(1) In each of the above embodiments, a two-dimensional image is generated using a two-dimensional fractal grid.
A three-dimensional stereoscopic image may be generated using a three-dimensional fractal grid, and the two-dimensional image may be generated by projecting the three-dimensional stereoscopic image on a two-dimensional plane.

(2) In §3 and §4, the method of generating the repeatable fractal lattice was briefly explained, but this method is generally called the "random midpoint displacement method". In addition to this, various methods such as a "fast Fourier transform filtering method" and a "sequential random addition method" are known as methods for generating a fractal lattice. Therefore, it is possible to generate the repeatable fractal grid by a method other than the “random midpoint displacement method”. Whatever method is used, it is possible to generate the printed matter according to the present invention as long as a repeatable fractal grid can be generated as a result.

(3) As a method of generating a unit image using the scalar field of the unit fractal lattice, §7, §
Although the methods specific to each of them are disclosed in 8 and §9, the present invention is not limited to these methods.
In short, any method may be used as long as it can generate a unit image having a natural fluctuation component of the unit fractal grid.

[0090]

As described above, according to the present invention, a unit image is created based on a unit fractal grid, and an image is generated by arranging a plurality of unit images spatially. It is possible to provide an image having mochi, and in which repeating patterns are continuously arranged.

[Brief description of drawings]

FIG. 1 is a diagram showing a 0th stage state in which a one-dimensional fractal lattice is generated.

FIG. 2 is a diagram showing a state of a first stage in which a one-dimensional fractal lattice is generated.

FIG. 3 is a diagram showing a second stage state in which a one-dimensional fractal lattice is generated.

FIG. 4 is a diagram showing specific scalar values defined at each grid point in the 0th stage of generating a one-dimensional fractal grid.

FIG. 5 is a diagram showing specific scalar values defined at each grid point in the first stage of generating a one-dimensional fractal grid.

FIG. 6 is a diagram showing specific scalar values defined at each grid point in the second stage of generating a one-dimensional fractal grid.

FIG. 7 is a diagram showing specific scalar values defined for each grid point in a one-dimensional fractal grid composed of five grid points.

FIG. 8 is a graph showing a natural fluctuation of a one-dimensional fractal grid composed of many grid points.

FIG. 9 is a diagram showing a state of the 0th stage of generating a two-dimensional unit fractal lattice.

FIG. 10: First to generate a two-dimensional unit fractal lattice
It is a figure which shows the state of a stage.

FIG. 11: Second for generating a two-dimensional unit fractal lattice
It is a figure which shows the state of a stage.

FIG. 12 is a diagram showing a basic structure of a two-dimensional unit fractal lattice.

FIG. 13 is a diagram showing a state in which a two-dimensional synthetic fractal lattice is formed by arranging a plurality of two-dimensional unit fractal lattices shown in FIG. 12 on a plane.

FIG. 14 is a diagram illustrating a basic principle of generating a repeatable two-dimensional unit fractal lattice in the present invention.

FIG. 15 is a diagram showing a 0th stage state in which a repeatable two-dimensional unit fractal lattice is generated.

FIG. 16 is a diagram showing a state of the first stage in which a repeatable two-dimensional unit fractal lattice is generated.

FIG. 17 is a diagram showing a second stage state in which a repeatable two-dimensional unit fractal lattice is generated.

FIG. 18 is a diagram showing another aspect of forming a two-dimensional synthetic fractal lattice by arranging a plurality of the two-dimensional unit fractal lattices shown in FIG. 12 on a plane.

FIG. 19 is a diagram illustrating a basic principle of generating a repeatable two-dimensional unit fractal lattice when the arrangement is performed in the mode shown in FIG.

FIG. 20 is a flowchart showing a general procedure for generating a repeatable unit fractal lattice in the present invention.

FIG. 21 is a block diagram showing a basic configuration of a printed matter creating apparatus according to the present invention.

FIG. 22 is a diagram illustrating a geometrical principle for artificially generating an annual ring pattern.

FIG. 23 is a diagram showing an example of an annual ring pattern generated based on the principle shown in FIG. 22.

FIG. 24 is a diagram showing a method of converting an original unit image P into a unit image Q having a natural fluctuation by utilizing a fractal grid F in the present invention.

25 is a diagram illustrating that a unit image Q having a repeatable pattern can be obtained by using a repeatable fractal grid in the method shown in FIG.

FIG. 26 is a diagram showing a state in which a three-dimensional stereoscopic image is cut along a wrinkled surface.

27 is a diagram showing a pattern obtained by projecting the wrinkled surface shown in FIG. 26 on a plane.

[Explanation of symbols]

1 ... Fractal condition setting section 2 ... Random number generator 3 Scalar value calculator 4 ... Scalar diversion part 5 ... Fractal grid generator 6 ... Pattern condition setting section 7 ... Image generation unit 8 ... Image printing section 10 ... Two-dimensional unit fractal lattice 11 ... Lattice points 12 ... Grid points on the right side 13 ... Lattice points on the left side 14 ... Lattice points on the lower side 15 ... Lattice points on the lower side that are offset by W 16 ... Lattice points on the upper side 17 ... Grid points on the lower side 18 ... Lattice points on the lower side that are offset by W 19 ... Lattice points on the upper side 20 ... Two-dimensional synthetic fractal lattice 30 ... Two-dimensional unit fractal lattice 31 ... Left side of external rectangle 32 ... right side of outer rectangle 33 ... the upper side of the external rectangle 34 ... Lower side of outer rectangle 35 ... Lattice points on the lower side 36 ... Lattice points on the upper side 37 ... Lattice points on the right side 38 ... Lattice points on the left side 40, 45 ... Concentric cylinders 50 ... XY plane 51 ... Annual ring pattern 60 ... Wrinkled surface 61 ... An annual ring pattern with fluctuations 65 ... Projection plane

Front page continuation (72) Inventor Ieji Hashizume 1-1-1, Ichigaya-Kagacho, Shinjuku-ku, Tokyo Within Dai Nippon Printing Co., Ltd. (72) 1-1-1 Ichigaya-Kagacho, Shinjuku-ku, Tokyo Issue Dai Nippon Printing Co., Ltd. (72) Inventor Yu Okamoto 1-1-1, Ichigaya-Kagacho, Shinjuku-ku, Tokyo Within Dai Nippon Printing Co., Ltd. (72) Inventor Yoshio Sukegawa 311 Takemazawa, Miyoshi-cho, Iruma-gun, Saitama Incorporated in Dainippon Total Process Building Materials (72) Inventor Hideki Murota 1-1-1 Ichigayakaga-cho, Shinjuku-ku, Tokyo Dai Nippon Printing Co., Ltd. (56) Reference JP-A-4-133183 (JP, A) JP-A-6-52277 (JP, A) (58) Fields investigated (Int.Cl. ⁷ , DB name) G06T 11/00 100

Claims (9)

(57) [Claims] 1. A unit fractal lattice in which a predetermined scalar value is self-similarly defined at each lattice point, and when a plurality of unit fractal lattices are spatially arranged, the boundary portion of each unit fractal lattice is Using a means to generate a repeatable unit fractal grid in which each scalar value is defined so as to be continuously connected, and each scalar value distributed in this repeatable unit fractal grid, within a predetermined unit area means for generating a unit image consisting of distributed pixels, by arranging a plurality of the unit image spatially, means for generating a composite image spatial repetition pattern has been expressed
When, repeating pattern, characterized in that it comprises an image having
Creation device . 2. A two-dimensional unit fractal lattice in which a predetermined scalar value is self-similarly defined at each lattice point on the two-dimensional plane, and when a plurality of the two-dimensional unit fractal lattices are arranged on the plane, Generate a repeatable 2D unit fractal grid in which each scalar value is defined so that the boundary part of each 2D unit fractal grid is continuously connected.
Means for generating a unit image composed of pixels distributed in a predetermined plane area by using each scalar value distributed in the repeatable two-dimensional unit fractal grid, and the unit image on a plane. Means for generating a composite image in which a planar repeating pattern is expressed by arranging a plurality of arrays
When, repeating pattern, characterized in that it comprises an image having
Creation device . 3. The image creating device according to claim 2 , wherein the repeating two-dimensional unit fractal grid is generated.
But based on the scalar value with the set defining the lattice point of the 0 stage having a predetermined scalar value at a predetermined position in accordance with the operation, the (i-1) stage lattice points defined by the external Then, the operation of giving a predetermined scalar value to the grid point defined in the i-th step is repeatedly executed until the parameter i reaches the predetermined value n while increasing the parameter i by 1 from the initial value 1, , When giving a predetermined scalar value to each grid point, for grid points on the first boundary side of the grid,
The same scalar value as that given to the grid point at the connection corresponding position on the second boundary side facing the first boundary side is given, and this grid value is given to the grid point on the third boundary side of the grid. It has a function of generating a repeatable two-dimensional unit fractal grid by giving the same scalar value as the scalar value given to the grid point at the connection corresponding position on the fourth boundary side facing the third boundary side. A device for creating images with repeating patterns. 4. The image creating apparatus according to claim 3 , wherein the repeating two-dimensional unit fractal grid is generated.
However, according to the setting operation from the outside , four grid points of the 0th stage having the same scalar value are defined at the four corner positions of the outer shape rectangle forming the outer shape of the grid, respectively. ) Recognize the minimum rectangle at the current stage that does not include the grid points defined up to the step), and define it at the midpoint of each side of this minimum rectangle and the center point of this minimum rectangle in the ith stage, respectively. A grid point is generated, and the grid point generated at the midpoint of each side is the (i-th) existing at the end point of the side.
1) Give a scalar value obtained by applying a random number to the scalar values of the two grid points defined up to the step, and for the grid point generated at the center point of the minimum rectangle, the four corner positions of the minimum rectangle. The scalar value obtained by applying a random number to the scalar values of the four lattice points defined up to the (i-1) th stage existing in is given to the lattice point defined in the i-th stage. Is performed by increasing the parameter i from the initial value 1 by 1 until the parameter i reaches a predetermined value n. In the work, the side of the smallest rectangle is the outer shape. When it matches the first side of the rectangle, the grid point generated at the midpoint of the side of the minimum rectangle is the second point of the outer shape rectangle facing the first side.
If the scalar value is the same as the scalar value given to the grid point at the connection corresponding position on the side of, and if the side of the minimum rectangle matches the third side of the outline rectangle, the midpoint of the side of this minimum rectangle For the grid points generated in the above, the fourth point of the outer shape rectangle facing the third side is
Of by giving the same scalar value as the scalar value given for the lattice points of connection corresponding positions on the sides of the image with a repeated pattern characterized by having the ability to produce a repeatable two-dimensional unit fractal grid Creation device . 5. The image according to any one of claims 2 to 4 .
In the creating device , the unit for generating the unit image is configured such that each grid point forming the repeatable two-dimensional unit fractal grid is associated with each pixel distributed in a predetermined rectangular area, and each pixel has a corresponding grid. An apparatus for creating an image having a repetitive pattern, wherein a unit image is generated by defining a pixel value corresponding to a scalar value of a point. 6. The image according to any one of claims 2 to 4 .
In creating apparatus, means for generating a repeatable two-dimensional unit fractal grid
Is the grid point F at the coordinate position (x, y) on the XY two-dimensional plane.
A unit for generating a repeatable two-dimensional unit fractal grid formed by arranging (x, y) and generating a unit image is a pixel P having a predetermined pixel value.
Based on the first image P formed by arranging (x, y) at the coordinate position (x, y) on the XY two-dimensional plane.
And has a function of generating a second image Q configured by arranging a pixel Q (x, y) having a predetermined pixel value at a coordinate position (x, y) on an XY two-dimensional plane , In generating the second image Q, for the pixel Q (x, y) arranged at the coordinate position (x, y), the grid point F (x, y) arranged at the coordinate position (x, y) is generated. ), The displacement amount d according to the scalar value defined for
Pixel P (x + d, y) arranged at coordinate position (x + d, y)
y) is specified as a reference pixel, and this reference pixel P (x +
An apparatus for creating an image having a repetitive pattern, characterized in that the second image Q is completed by giving the pixel value Z of d, y) to the pixel Q (x, y). 7. The image according to any one of claims 2 to 4 .
In creating apparatus, means for generating a repeatable two-dimensional unit fractal grid
Is the grid point F at the coordinate position (x, y) on the XY two-dimensional plane.
A unit for generating a repeatable two-dimensional unit fractal grid formed by arranging (x, y) and generating a unit image has a predetermined surface in accordance with a scalar value of each grid point of the two-dimensional unit fractal grid. A wrinkled surface is formed by displacing each point in a predetermined direction, and a three-dimensional stereoscopic image configured by arranging pixels having a predetermined pixel value in an XYZ three-dimensional space is input. image cut by the chromatic wrinkles surface, having a repeating pattern and generates unit image by projecting pixels appearing on the cut surface onto a planar image
Creation device . 8. A fractal condition setting unit for setting conditions necessary for generating a unit fractal grid, and a random number generator for generating random numbers for giving fluctuation to a scalar value given to each grid point forming the unit fractal grid. And a condition set in the fractal condition setting unit,
Random number generated by the random number generation unit, by a predetermined calculation based on a scalar value calculation unit that calculates a scalar value to be given to each grid point, when a plurality of unit fractal grids generated are spatially arranged, A scalar value diversion unit that diverts a scalar value to be given to a predetermined lattice point of the boundary portion from a scalar value of another lattice point so that the boundary portions of individual unit fractal lattices are continuously connected, and the scalar value. A unit formed by giving a predetermined scalar value to each grid point in a self-similar manner by giving each grid point either a scalar value calculated by the calculation unit or a scalar value converted by the scalar value conversion unit. A fractal grid generation unit that generates a fractal grid, and a pattern condition setting unit that sets the conditions necessary to generate a unit pattern expressed as a printed matter. From the pixels distributed in the predetermined unit area by a predetermined calculation based on each scalar value distributed in the unit fractal grid generated by the fractal grid generation unit and the condition set in the pattern condition setting unit. generates unit image consisting, by arranging a plurality of the unit image spatially, with the repetitive pattern, characterized in that it comprises an image generator for generating a composite image that spatial repetition pattern has been expressed, the Image creation device. 9. The image creating apparatus according to claim 8 , wherein the fractal condition setting unit includes a size of a unit fractal grid to be generated, a maximum half amplitude value T, and an external rectangle 4 forming an external shape of the grid. The fractal grid generating unit has a function of setting initial grid points having the same scalar value arranged at each corner position as conditions, and the fractal grid generation unit has a middle point of two adjacent grid points and another grid point. Has a function to define a new grid point at the center point of the four grid points that form the smallest rectangle that does not include inside, and the scalar value calculation unit uses the new grid point defined at the midpoint of the two grid points. As the scalar value to be given to the point, the average value of the scalar values of the two grid points and the maximum half amplitude value T or its (1
/ 2 ⁿ ) and the total value of and, as the scalar value to be given to the new grid point defined at the center point of the four grid points, the scalar values of the four grid points are given. An average value and a number obtained by multiplying the random number generated by the random number generation unit by the maximum half-amplitude value T or the value of (1/2 ⁿ ) thereof;
Using the total value of, the scalar value diversion part uses a scalar value to be diverted to the grid point of the boundary part, and if the generated unit fractal grids are spatially arranged in multiple numbers, the other boundary parts Using the scalar value given to the grid point, the fractal grid generation unit repeatedly executes the process of defining a new grid point until the size set in the fractal condition setting unit is obtained, and a new definition is made. If the grid point is on the first side of the outline rectangle or the second side orthogonal thereto, the scalar value diverted by the scalar value diversion unit is given to this grid point to newly define the grid point. Is not on the first side or the second side, a repetitive pattern characterized by performing a process of giving a scalar value calculated by the scalar value calculation unit to this grid point Image creation apparatus.