CN101739700A - Anti-counterfeiting pattern manufacturing method using fractal pattern to overlap fractal curve - Google Patents
Anti-counterfeiting pattern manufacturing method using fractal pattern to overlap fractal curve Download PDFInfo
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Abstract
The invention discloses an anti-counterfeiting pattern manufacturing method using a fractal pattern to overlap a fractal curve. The pattern manufacturing is finished by two methods, namely the manufacturing of the fractal pattern and the manufacturing of a pattern of the fractal curve. The method comprises the concrete steps of: (1) the manufacturing of the fractal pattern, which comprises the steps of: adopting a mathematical formula to set parameter information and color matching information in a computer drawing panel, and drawing the fractal pattern in the computer drawing panel; (2) the manufacturing of the pattern of the fractal curve, which comprises the steps of: 1, setting an alphabet V, an initial axiom omega and a generative rule P in a computer fractal curve drawing panel; and 2, then setting initial point coordinates (x, y) in the drawing panel in the step 1 to establish the circulation of iteration number n and execute the iteration number from 1 to n, and searching each character in a new character string F produced in the step 3 in sequence; and (3) performing graph overlapping on the fractal pattern manufactured in the step (1) and the pattern of the fractal curve manufactured in the step (2) in the computer drawing panel to obtain an anti-counterfeiting pattern. The method can resist reprography in combination with the embedded fractal curve and special ink printing technology to realize the double anti-counterfeiting function.
Description
Technical field
The present invention relates to the making of pattern, be specially a kind of method for making of fractal security pattern.
Background technology
At present, known fractal pattern method for drafting is to set an iterative formula by the designer, and programming realizes method for drafting, and sets suitable scheme of colour therein, generates pattern at last.But the pattern that generates is when being used for the security pattern design, and anti-replication capacity is limited.The security pattern of the graftal stack fractal curve that the present invention makes in conjunction with complicated fractal pattern and specialty inks printing technology, not only can't be repaired by other graph and image processing systems, and can resist duplicating, has the double anti-forge function.
Summary of the invention
The security pattern method for making that the purpose of this invention is to provide a kind of graftal stack fractal curve, it can overcome the deficiency of aspects such as existing fractal pattern method for drafting is lack of standardization, too high to drafting personnel or the requirement of design personnel specialty level, the design cycle is long, provides a kind of user of making only just can draw out the method for complicated security pattern by easy operation.The special lines that the present invention utilizes fractal curve to form embed in the multiple iteration fractal pattern.The fractal curve of this self similarity generates flexibly, stronger regularity is arranged at random, and is no lack of randomness in the rule.Flickering in the comparatively peculiar multiple iteration graftal of shape and color configuration, in conjunction with the printing-ink printing technology, can resist duplicating.And the labyrinth of fractal pattern itself can't be repaired it by other graph and image processing systems.Left corresponding formula and parameter, fractal pattern can not be copied fully, thereby has realized the double anti-forge function.
The present invention is achieved through the following technical solutions: a kind of security pattern method for making of graftal stack fractal curve is characterized in that: its design producing is made by fractal pattern and two kinds of methods of fractal curve design producing are finished, and concrete steps are:
(1) fractal pattern making step:
1. adopt mathematical formulae setup parameter information in the computerized mapping panel, its formula is multiple iterative formula Z=f (Z)+C of generalized M-J ensemble figure, and wherein, f (Z) is sin (Z), cos (Z), tg (Z), ctg (Z), e
Z, Z
k, and
Express formula for the arithmetical operation of elementary function, Z is a complex variable in the expression formula, and C is multiple constant, and k is a real constant; Comprise factor, the factor and the various parameters among them in the formula;
2. in the computerized mapping panel, set color matching information, what computing machine adopted all is rgb color technology, the conversion formula of initial look by setting pattern and 3 primary colours R, G, B forms scheme of colour information, described conversion formula is: cos (x), log (x), log (y*y), log (x/y), log (log (y*)), sin (log (d*d)), tg (log (d*d)), sin (log (x*x)) and log (sin (y)), wherein d is the air line distance of adjacent point-to-point transmission, and x, y are respectively the projection of d on x axle, y axle; Described RGB three primary colours color range 0～255;
3. in the computerized mapping panel, draw fractal pattern, finish by determining drawing algorithm and algorithm parameter thereof, described drawing algorithm adopts the escape time algorithm, the escape algorithm is: the iteration zone W of given computer screen representative, escape radius R and maximum iterations N, radius R＞0 of wherein escaping, iterations N＞0; The formula of the definition escape function of time is:
Formula-1
To the some c in the iteration zone, calculate T (c); If T (c)=0, then c ∈ M
1If T (c) ≠ 0, then c ∈ M
2According to the value of T (c), i and k and the color of previous point thereof, determine the color of current some c.M
1And M
2The color of being had a few in the zone promptly constitutes desired pattern;
4. adopt the coordinate information that draws a design in the computerized mapping panel, coordinate information is two, and one is the coordinate information of complex plane, and one is the view information of window on the computer screen; Define by lower-left, upper right two the apex coordinate values of determining rectangle frame; 1. set the parameter information of mathematical formulae formation and the combination of the color matching information that 2. step is set by step at last, again by step 3. drawing algorithm information and step 4. two coordinate informations of pattern-making finish the final drafting of figure, it is standby to form fractal pattern;
(2) fractal curve design producing step:
1. in Computer Fractal curve drawing panel, set alphabet V, initial axiom ω, create-rule P is as alphabet V:F, initial axiom ω: F, P:F → F-F++F-F;
2. in 1. step charts panel, be provided with again the initial point coordinate (x, y), the step-length F that each walking is walked, anglec of rotation δ: 60 °, and iterations n;
3. iterations n is set up circulation and carry out, in loop body, search for a character string F$, and utilize expression formula F$=" F-F++F-F " that character " F " is wherein replaced, after the loop ends, then generate a new character strings F$ from 1-n.
4. each character among the new character strings F$ that 3. produced of search step in order if show "+", then is rotated counterclockwise 60 °; Show "-", then turn clockwise 60 °; Show " F " that then draw straight line along current direction, until character string caudal knot bundle, thereby the fractal curve that draws is made the fractal curve pattern;
(3) security pattern is made in fractal pattern of in the computerized mapping panel step (1) being made and step (2) the fractal curve graphic design stack of making.
Advantage of the present invention is: 1. fractal pattern and fractal curve are to be generated by computing machine, its advantage is to generate the complicated pattern that very strong artistic feeling is arranged according to simple uninteresting mathematical formulae, between the pattern that generates and the mathematical information being---corresponding relation provides pattern to originate by formula and the parameter that changes in the mathematical information.2. the mathematical information of fractal pattern can be determined arbitrarily by the user.3. embed fractal curve in the fractal pattern, good anti-copy function is arranged.
The present invention utilizes computer program to realize that the user sets up iterative formula on their own by the selected formula factor, change function by selected priming color and R (red), G (green), 3 kinds of primary colours of B (indigo plant) and set up the color change rule on their own, set suitable method for drafting by selected algorithm and algorithm parameter, set drawing area and show view by selected complex plane and screen coordinate, thereby can easily draw generalized M-J ensemble pattern.
Lines in the graftal that the present invention is made in the partial view can show tangible stereovision, and the complicacy of its structure makes other people to repair by other graph and image processing systems, away from original formula and parameter, can not be imitated fully.Fractal curve and specialty inks printing technology in conjunction with embedding can resist duplicating, realize the double anti-forge function.
Description of drawings
Fig. 1 is design producing panel figure of the present invention; Fig. 2 is curve plotting panel figure of the present invention; A kind of pattern form of Fig. 3 for adopting method for drafting of the present invention to draw out; A kind of curve of Fig. 4 for adopting method for drafting of the present invention to draw; Fig. 5 is for adopting the final pattern of method for drafting of the present invention with fractal pattern and fractal curve stack back generation.Fig. 6 is the parameter among Fig. 1 for a change, produces another pattern that produces with fractal curve stack back behind the fractal pattern.
Embodiment
The present invention is further described below in conjunction with drawings and Examples.
The security pattern method for making of a kind of graftal stack fractal curve of the present invention, the fractal pattern manufacturing system that utilizing has programmed realizes generates pattern, and concrete steps are as follows:
(1) fractal pattern making step:
1. adopt mathematical formulae setup parameter information in the computerized mapping panel, its formula is multiple iterative formula Z=f (Z)+C of generalized M-J ensemble figure, and wherein, f (Z) is sin (Z), cos (Z), tg (Z), ctg (Z), e
Z, Z
k, and
Express formula for the arithmetical operation of elementary function, Z is a complex variable in the expression formula, and C is multiple constant, and k is a real constant; Comprise factor, the factor and the various parameters among them in the formula;
2. in the computerized mapping panel, set color matching information, what computing machine adopted all is rgb color technology, the conversion formula of initial look by setting pattern and 3 primary colours R, G, B forms scheme of colour information, described conversion formula is: cos (x), log (x), log (y*y), log (x/y), log (log (y*y)), sin (log (d*d)), tg (log (d*d)), sin (log (x*x)) and log (sin (y)), wherein d is the air line distance of adjacent point-to-point transmission, and x, y are respectively the projection of d on x axle, y axle; Described RGB three primary colours color range 0～255;
3. in the computerized mapping panel, draw fractal pattern, finish by determining drawing algorithm and algorithm parameter thereof, described drawing algorithm adopts the escape time algorithm, the escape algorithm is: the iteration zone W of given computer screen representative, escape radius R and maximum iterations N, radius R＞0 of wherein escaping, iterations N＞0; The formula of the definition escape function of time is:
To the some c in the iteration zone, calculate T (c); If T (c)=0, then c ∈ M
1If T (c) ≠ 0, then c ∈ M
2According to the value of T (c), i and k and the color of previous point thereof, determine the color of current some c.M
1And M
2The color of being had a few in the zone promptly constitutes desired pattern;
4. adopt the coordinate information that draws a design in the computerized mapping panel, coordinate information is two, and one is the coordinate information of complex plane, and one is the view information of window on the computer screen; Define by lower-left, upper right two the apex coordinate values of determining rectangle frame; 1. set the parameter information of mathematical formulae formation and the combination of the color matching information that 2. step is set by step at last, again by step 3. drawing algorithm information and step 4. two coordinate informations of pattern-making finish the final drafting of figure, it is standby to form fractal pattern;
(2) fractal curve design producing step:
1. in Computer Fractal curve drawing panel, set alphabet V, initial axiom ω, create-rule P is as alphabet V:F, initial axiom ω: F, P:F → F-F++F-F;
2. in 1. step charts panel, be provided with again the initial point coordinate (x, y), the step-length F that each walking is walked, anglec of rotation δ: 60 °, and iterations n;
3. iterations n is set up circulation and carry out, in loop body, search for a character string F$, and utilize expression formula F$=" F-F++F-F " that character " F " is wherein replaced, after the loop ends, then generate a new character strings F$ from 1-n.
4. each character among the new character strings F$ that 3. produced of search step in order if show "+", then is rotated counterclockwise 60 °; Show "-", then turn clockwise 60 °; Show " F " that then draw straight line along current direction, until character string caudal knot bundle, thereby the fractal curve that draws is made the fractal curve pattern;
(3) security pattern is made in fractal pattern of in the computerized mapping panel step (1) being made and step (2) the fractal curve graphic design stack of making.
When the present invention used, the user was to select the formula factor, combined iteration formula voluntarily on Fig. 1 at the design producing panel; Set priming color value and R (red), G (green), 3 kinds of primary colours variations of B (indigo plant) function, determine the color matching parameter; Select method for drafting, determine relevant parameter; Select drawing area and show view by setting complex plane and screen coordinate; Click " drafting " and generate fractal pattern, as shown in Figure 3; It is the fractal curve type that selection will be drawn on Fig. 2 that the user makes panel at fractal curve; Set the iterations of fractal curve; Set the property parameters of fractal curve, comprise the fineness of coordinate, lines and the color of lines; It is promptly shown in Figure 4 to click " drafting " generation fractal curve; By synthetic fractal pattern of design proposal management and fractal curve, promptly generate the figure that pattern of the present invention is Fig. 5.The present invention utilizes computer program to realize that the user sets up iterative formula on their own by the selected formula factor, change function by selected priming color and R (red), G (green), 3 kinds of primary colours of B (indigo plant) and set up the color change rule on their own, set suitable method for drafting by selected algorithm and algorithm parameter, set drawing area and show view by selected complex plane and screen coordinate, thereby can easily draw generalized M-J ensemble pattern.
M-J collection pattern of the present invention is the abbreviation of Mandelbrot set and Julia set, is known technology.
Embodiment 1
Adopt multiple iterative formula when drawing a design, the setting formula is: cos (z)-a/z (k) (a=2).Drawing practice is selected " the time radius method of escaping ", type selecting Julia set; The complex plane coordinate parameters is set at (1.5 ,-1.5), (1.5,1.5); Initial value design is: X is 0.32, Y is 0.04, and iterations is set at 10, and index K is set at 2.Set scheme of colour information then, the conversion formula of the initial look of pattern and 3 primary colours R, G, B is set in " colouration scheme " selection " theme ".Wherein the R initial value is 216, and R changes item and calculates definite by formula log (x); The G initial value is 32, and G changes item and calculates definite by formula log (log (y*y)); The B initial value is 125, and B changes item and calculates definite by formula sin (log (d*d)).The gradual change step-length is 0.5, clicks the fractal pattern that " drawing " key can obtain Fig. 3 at last.
Embodiment 2
Make in the panel at fractal curve, fractal curve is set at " imperial crown ", iterations is set at 5, and line thickness is set at 3.Click " beginning mouse select ", drag mouse and determine starting point and terminating point, paint fractal curve.Along different direction drag and drop mouses twice, can obtain the fractal curve of Fig. 4.
Embodiment 3
In the design proposal management, import Fig. 3 and Fig. 4.Select Fig. 3 to scheme as a setting, Fig. 4 is as foreground picture, and R, G, B three look masking values are made as 100%, and transparency is made as 40%.Click " synthesizing ", generate the pattern form of Fig. 5 correspondence.Fig. 5 promptly is a complete pattern of the present invention.
Embodiment 4
Fig. 6 is another complete pattern of the present invention.It obtains by fractal pattern A and fractal curve B are synthetic.Adopt multiple iterative formula when drawing fractal pattern A, the setting formula is: tan (z)/cos (z).Drawing practice is selected " the time radius method of escaping ", type selecting Julia set; The complex plane parameter setting is (1.5 ,-1.5), (1.5,1.5); Initial value design is: X is 0.32, Y is 0.04, and iterations is 2, and index K is set at 10.Set scheme of colour information then, set the conversion formula of the initial look of pattern and 3 primary colours R, G, B.Wherein the R initial value is 125, and R changes item and calculates definite by formula log (x); The G initial value is 25, and G changes item and calculates definite by formula log (log (y*y)); The B initial value is 215, and B changes item and calculates definite by formula sin (log (d*d)).The gradual change step-length is made as 1, clicks " drafting " key at last and can obtain A.When drawing fractal curve B, make in the panel at fractal curve, fractal curve is set at " imperial crown ", iterations is set to 5, and line thickness is made as 3.Click " beginning mouse select " at last, drag mouse and determine starting point and terminating point, paint fractal curve.Along different direction drag and drop mouse 2 times, can obtain B.In the design proposal management, import A and B.Select A to scheme as a setting, B is as foreground picture, and R, G, B three look masking values are made as 100%, and transparency is made as 40%.Click " synthesizing ", generate the pattern form of Fig. 6 correspondence, obtain product pattern of the present invention.
Claims (1)
1. the security pattern method for making of graftal stack fractal curve, it is characterized in that: its design producing is made by fractal pattern and two kinds of methods of fractal curve design producing are finished, and concrete steps are:
(1) fractal pattern making step:
1. adopt mathematical formulae setup parameter information in the computerized mapping panel, its formula is multiple iterative formula Z=f (Z)+C of generalized M-J ensemble figure, and wherein, f (Z) is sin (Z/), cos (Z), tg (Z), ctg (Z), e
Z, Z
k, and
Express formula for the arithmetical operation of elementary function, Z is a complex variable in the expression formula, and C is multiple constant, and k is a real constant; Comprise factor, the factor and the various parameters among them in the formula;
2. in the computerized mapping panel, set color matching information, what computing machine adopted all is rgb color technology, the conversion formula of initial look by setting pattern and 3 primary colours R, G, B forms scheme of colour information, described conversion formula is: cos (x), log (x), log (y*y), log (x/y), log (log (y*y)), sin (log (d*d)), tg (log (d*d)), sin (log (x*x)) and log (sin (y)), wherein d is the air line distance of adjacent point-to-point transmission, and x, y are respectively the projection of d on x axle, y axle; Described RGB three primary colours color range 0～255;
3. in the computerized mapping panel, draw fractal pattern, finish by determining drawing algorithm and algorithm parameter thereof, described drawing algorithm adopts the escape time algorithm, the escape algorithm is: the iteration zone W of given computer screen representative, escape radius R and maximum iterations N, radius R＞0 of wherein escaping, iterations N＞0; The formula of the definition escape function of time is:
To the some c in the iteration zone, calculate T (c); If T (c)=0, then c ∈ M
1If T (c) ≠ 0, then c ∈ M
2According to the value of T (c), i and k and the color of previous point thereof, determine the color of current some c.M
1And M
2The color of being had a few in the zone promptly constitutes desired pattern;
4. adopt the coordinate information that draws a design in the computerized mapping panel, coordinate information is two, and one is the coordinate information of complex plane, and one is the view information of window on the computer screen; Define by lower-left, upper right two the apex coordinate values of determining rectangle frame; 1. set the parameter information of mathematical formulae formation and the combination of the color matching information that 2. step is set by step at last, again by step 3. drawing algorithm information and step 4. two coordinate informations of pattern-making finish the final drafting of figure, it is standby to form fractal pattern;
(2) fractal curve design producing step:
1. in Computer Fractal curve drawing panel, set alphabet V, initial axiom ω, create-rule P is as alphabet V:F, initial axiom ω: F, P:F → F-F++F-F;
2. in 1. step charts panel, be provided with again the initial point coordinate (x, y), the step-length F that each walking is walked, anglec of rotation δ: 60 °, and iterations n;
3. iterations n is set up circulation and carry out, in loop body, search for a character string F$, and utilize expression formula F$=" F-F++F-F " that character " F " is wherein replaced, after the loop ends, then generate a new character strings F$ from 1-n;
4. each character among the new character strings F$ that 3. produced of search step in order if show "+", then is rotated counterclockwise 60 °; Show "-", then turn clockwise 60 °; Show " F " that then draw straight line along current direction, until character string caudal knot bundle, thereby the fractal curve that draws is made the fractal curve pattern;
(3) security pattern is made in fractal pattern of in the computerized mapping panel step (1) being made and step (2) the fractal curve graphic design stack of making.
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| CN102708391A (en) * | 2012-05-14 | 2012-10-03 | 华南农业大学 | Anti-counterfeiting label on basis of fractal image and anti-counterfeiting verification method |
| CN103903289A (en) * | 2014-04-02 | 2014-07-02 | 中国地质大学（武汉） | Stochastic pattern wetland pattern generating method based on fractal generator |
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| CN107358634A (en) * | 2017-06-26 | 2017-11-17 | 宁德师范学院 | The color rendering intent and device of a kind of fractal pattern |
| CN110288066A (en) * | 2019-06-12 | 2019-09-27 | 广州鼎宁信息科技有限公司 | A kind of generation of the fractal graph collection based on root function and parameter detection method |
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2009
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| CN102708391A (en) * | 2012-05-14 | 2012-10-03 | 华南农业大学 | Anti-counterfeiting label on basis of fractal image and anti-counterfeiting verification method |
| CN102708391B (en) * | 2012-05-14 | 2015-08-19 | 华南农业大学 | A kind of antifalsification label based on fractal graph and anti-counterfeit authentication method |
| CN103903289A (en) * | 2014-04-02 | 2014-07-02 | 中国地质大学（武汉） | Stochastic pattern wetland pattern generating method based on fractal generator |
| CN103903289B (en) * | 2014-04-02 | 2015-03-04 | 中国地质大学（武汉） | Stochastic pattern wetland pattern generating method based on fractal generator |
| CN106157059A (en) * | 2016-07-07 | 2016-11-23 | 山东师范大学 | A kind of based on graphics safegurard mark false-proof detection method and system thereof |
| CN106815799A (en) * | 2016-12-19 | 2017-06-09 | 浙江画之都文化创意股份有限公司 | A kind of self adaptation artistic pattern forming method based on chaology |
| CN106815799B (en) * | 2016-12-19 | 2020-01-21 | 浙江画之都文化创意股份有限公司 | Chaos theory-based adaptive art pattern generation method |
| CN107358634A (en) * | 2017-06-26 | 2017-11-17 | 宁德师范学院 | The color rendering intent and device of a kind of fractal pattern |
| CN110288066A (en) * | 2019-06-12 | 2019-09-27 | 广州鼎宁信息科技有限公司 | A kind of generation of the fractal graph collection based on root function and parameter detection method |
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