CN103177461B - Artistic pattern forming method based on fractal cloud model cellular automata - Google Patents

Abstract

A kind of artistic pattern forming method based on fractal cloud model cellular automata, is used for generating existing overall fractal effect, has again details uncertainty art pattern.Its technical scheme is, input picture after initialization is processed by described method carries out q fractal matrix iteration, and before each fractal matrix iteration, first carry out p cloud model cellular automata evolution, generate a large amount of existing overall fractal effect, there is again the probabilistic art pattern of details.Cloud model cellular automata is combined by the present invention with fractal matrix method, generate process at pattern and simultaneously take account of ambiguity and randomness, so that the art pattern generated is fractal on the whole, uncertain difference is had again in details, giving new visual experience, the diversity of this details disclosure satisfy that people are to beautiful individual needs.

Description

Artistic pattern forming method based on fractal cloud model cellular automata

Technical field

The present invention relates to one to generate existing overall fractal effect, again there is details uncertainty art figure The method of case, belongs to technical field of data processing.

Background technology

Art pattern design is a kind of modeling activity for the purpose of plane decoration, utilizes the fractal art that carries out to scheme Case design has been great progress, and Fractal Artistic Patterns receives liking of people as a kind of artistic form.Should Carry out Design of Fractal Artistic Patterns with computer and depend greatly on pattern generating algorithm, these algorithms On the basis of being built upon the comprehensive utilization to composite principle and creation thought.The most basic Fractal Artistic Patterns Generating algorithm mainly includes two classes: a class is to use function iteration and repeated application algorithm based on aggregation process； Another kind of, it is to use the traditional and fractal algorithm recompose-technique combined, such as overall fractal composition and rule bone Organization Chart method.The most overall fractal composition is, according to certain algorithm model, the breadth of pattern is carried out overall point Shape constructs, and to produce the picture with infinite self-similarity characteristics, fractal matrix is exactly a kind of typical overall point Shape patterning process, it uses the method for matrix iteration can obtain clearly as a kind of simple pattern generating algorithm The most beautiful fractal pattern.But this method excessively relies on generator matrix, so using identical generator matrix The art pattern obtained is similar, is difficult to satisfied being actually needed；Additionally fuzzy cellular automata is also employed Generating field in art pattern, its dynamic behavior can produce various complexity, beautiful art pattern, It avoids cellular automata unpredictability in generating patterning process by the constraint of fuzzy rule, makes Obtain cellular automata to develop to the direction of ideal pattern.The shortcoming of described method is only in initial pattern For the fractal pattern with infinite self-similarity characteristics could be produced during fractal pattern, which has limited its range of application； The present inventor is it is proposed that a kind of fractal fuzzy cellular automata artistic pattern forming method, and described method is by fractal Matrix and fuzzy cellular automata method combine, and use fuzzy cellular automatic before each iteration of fractal matrix Machine develops several times, so that described method has the feature of above two kinds of methods concurrently, it is possible to generation complexity, Beautiful and fractal art pattern.But, owing to described method only takes into account the ambiguity that cellular automata develops And do not consider randomness, make to develop that the pattern produced determines that, full symmetric and gestalt every time.Mesh The art pattern mentality of designing that former is new is " overall fractal but non complete symmetry or uncertain figure in details Case often gives people with new visual experience ", in view of fractal fuzzy cellular automata method for generating pattern Feature, it cannot generate this existing overall fractal effect and have again the probabilistic art pattern of details, institute Generate needs with the art pattern being difficult to meet under this mentality of designing, also limit its range of application.

Summary of the invention

Present invention aims to the drawback of prior art, it is provided that one is based on fractal cloud model cellular certainly The artistic pattern forming method of motivation, to generate existing overall fractal effect, has again details uncertainty skill Art pattern.

Problem of the present invention realizes with following technical proposals:

A kind of artistic pattern forming method based on fractal cloud model cellular automata, described method is to initialization Input picture after process carries out q fractal matrix iteration, and first carries out before each fractal matrix iteration P time cloud model cellular automata develops, and generates a large amount of existing overall fractal effect, has again details uncertain The art pattern of property, said method comprising the steps of:

A. initialization processes:

Input picture is carried out pretreatment, picture is converted to gray-scale map and by the gray value matrix of gained pattern As the original state matrix of cellular, then set cloud model cellular automata evolution number of times p and fractal matrix Iterations q；

B. use selected cloud rule of inference that pattern gray value matrix is carried out cloud reasoning；

C. according to cloud the reasoning results, pattern gray value matrix is carried out anti-cloudization to process；

D. according to anti-cloud result, pattern gray value matrix is carried out cellular automata evolution:

By the cloud the reasoning results E (y of each cellular₁) be added with this cellular state value of current time and to obtain lower a period of time The state value carved, thus generate the gray value matrix of subsequent time；

E. being judged whether evolution result meets its requirement by user, being deposited into art pattern storehouse if meeting the requirements；

F. judging whether evolution number of times reaches p time, proceeding to step b if not, if proceeding to step g；

G. pattern gray value matrix step f obtained, as generator matrix, carries out fractal matrix iteration:

Order matrix A is as the generator matrix of iterated transform, respectively with each element a of A_ij(1≤i≤m, 1≤j≤n) plus or be multiplied by the matrix of each element gained of matrix A, remove substitutional element a_ijItself, produce Giving birth to matrix A ＇, wherein m Yu n distinguishes line number and the columns of representing matrix

$A^{\′}=A\⊕A=\left[\begin{array}{ccc}{a}_{11}+A& ....& a_{1n}+A\\ ....& ....& ....\\ a_{m1}+A& ....& a_{mn}+A\end{array}\right],$

Or

H. judge whether iterations reaches q time, proceed to step b if not and using A ＇ as new pattern ash Angle value matrix, if then terminating.

Above-mentioned artistic pattern forming method based on fractal cloud model cellular automata, is carrying out Yun Mo to picture Use Normal Cloud that variable is carried out cloud when type cellular automata develops.

Cloud model cellular automata is combined by the present invention with fractal matrix method, generates process simultaneously at pattern In view of ambiguity and randomness, so that the art pattern generated is fractal on the whole, details has again Uncertain difference, gives new visual experience, and the diversity of this details disclosure satisfy that people are to U.S. Individual needs.

Accompanying drawing explanation

The invention will be further described below in conjunction with the accompanying drawings.

Fig. 1 is the flow chart of technical solution of the present invention；

Fig. 2 is the cloud reasoning device that art pattern generates；

Fig. 3 is 1 evolution art pattern generation result after (He=En/400) 3 iteration；

Fig. 4 is 3 evolution art patterns generation results after (He=En/400) 3 iteration；

Fig. 5 is 9 evolution art patterns generation results after (H=En/400) 3 iteration；

Fig. 6 is 1 evolution art pattern generation result after (He=En/200) 3 iteration；

Fig. 7 is 3 evolution art patterns generation results after (He=En/200) 3 iteration；

Fig. 8 is 9 evolution art patterns generation results after (H=En/200) 3 iteration；

Fig. 9 is 1 evolution art pattern generation result after (He=0) 3 iteration；

Figure 10 is 3 evolution art patterns generation results after (He=0) 3 iteration；

Figure 11 is 9 evolution art patterns generation results after (He=0) 3 iteration.

In literary composition, symbol inventory used is: p is cloud model cellular automata evolution number of times, and q is fractal matrix iteration Number of times, x1 and x2 is two input variables, and y1 is output variable, a_ijFor the element of matrix A, μ represents It is subordinate to angle value, CG_AijAnd CG_BkFor cloud generator, MP is multiplier, and RS is rule selector.

Detailed description of the invention

Step a is pre-treatment step, input picture is carried out pretreatment, picture is converted to gray-scale map and obtains Obtain the gray value matrix original state matrix as cellular of pattern, it is then determined that relevant parameter, such as cellular certainly Motivation evolution number of times p and fractal matrix iteration number of times q etc..

Step b, c, d belong to the step that cloud model cellular automata develops.Here cloud model cellular is introduced It is the most true that the purpose that automat develops is to use cloud model reasoning simulation human brain decision-making acquisition preferably to have details The most complicated, beautiful and fractal pattern.

Step b, c together constitute a complete cloud reasoning device, and each cellular is carried out cloud reasoning, as Shown in Fig. 2, before this many condition more rules reasoning device number of packages be 2, rule number be 9, be embodied as way as follows:

1) input vector cloud.Fig. 2 left-hand component is input vector cloud process, and the inventive method includes Two input variables: the gray value x1 and neighborhood cellular average gray value x2 of center cellular, each input becomes Corresponding three kinds of qualitativing concept (Linguistic Value): the A of amount₁={ grey level is low }, A₂={ grey level is medium }, A₃={ ash Degree level is high }, two input variables constitute input vector X.Cloudization for input vector passes through two dimension X Condition cloud generator realizes, and two dimension X condition cloud generator is expanded by one-dimensional X condition cloud generator. For different systems, the shape of cloud is probably different, and in view of the universality of Normal Cloud, the present invention uses Normal Cloud carries out cloud to variable.The most corresponding 9 kinds of sizings concept (Linguistic Value) of input vector: { x1 Linguistic Value For A₁, x2 Linguistic Value is A₁, { x1 Linguistic Value is A₂, x2 Linguistic Value is A₁, { x1 Linguistic Value is A₃, X2 Linguistic Value is A₁, { x1 Linguistic Value is A₁, x2 Linguistic Value is A₂, { x1 Linguistic Value is A₂, x2 language Speech value is A₂, { x1 Linguistic Value is A₃, x2 Linguistic Value is A₂, { x1 Linguistic Value is A₁, x2 Linguistic Value For A₃, { x1 Linguistic Value is A₂, x2 Linguistic Value is A₃, { x1 Linguistic Value is A₃, x2 Linguistic Value is A₃, The corresponding two-dimentional X condition cloud generator of each Linguistic Value, each two dimension X condition cloud generator is by two one Dimension X condition cloud generator CG_AijConstitute with 1 multiplier MP, wherein represent defeated respectively when i=1,2,3 Entering variable Linguistic Value is A₁、A₂And A₃, when j=1,2 time represent different input variables x1 and x2 respectively. Such as, { x1 Linguistic Value is A to first Linguistic Value of input vector₁, x2 Linguistic Value is A₁Corresponding two-dimentional X Condition cloud generator is by 2 one-dimensional X condition cloud generator CG_A11And CG_A12And 1 multiplier MP is constituted, CG_A11Represent the one-dimensional X condition cloud generator that the 1st Linguistic Value of input variable x1 is corresponding, CG_A12Represent input The one-dimensional X condition cloud generator that the 1st Linguistic Value of variable x2 is corresponding, μ₁₁And μ₁₂It is respectively CG_A11And CG_A12 Output degree of membership, μ₁₁And μ₁₂μ is obtained by multiplier MP₁=μ₁₁×μ₁₂, μ₁Represent and meet input The degree of membership of first Linguistic Value of vector.Other 8 input vector Linguistic Value degrees of membership μ₂..., μ₉Meter Calculation process and μ₁Calculating process be similar to, the one-dimensional X condition cloud generator simply used is different.

2) cloud rule of inference.This reasoning has output variable y1, and it includes 4 kinds of qualitativing concept (language Value): B₁={ small step degeneration }, B₂={ walking greatly degeneration }, B₃={ small step evolution }, B₄={ big stepping }, uses respectively In representing evolving and the degree degenerated of cellular.It is required to meet when any current time cellular is made inferences Following cloud rule of inference, as shown in table 1, rule number is 9,9 kinds of Linguistic Values of the most corresponding input vector.

The cloud rule of inference that table 1 art pattern generates

3) cloud reasoning.Fig. 2 mid portion is cloud reasoning process, degree of membership μ that input vector cloud obtains_m (m=1,2 ..., 9), represent that the activation degree of m article of qualitative rule, rule selector RS therefrom select respectively Maximum degree of membership μ_max, i.e. μ_maxCorresponding qualitative rule is selected, selects correspondence according to cloud rule of inference table Output language value as the reasoning results.

4) anti-cloudization output.Fig. 2 right-hand component is anti-cloud output procedure, by μ_maxValue brings corresponding output into The one-dimensional Y condition cloud generator CG of Linguistic Value_BkIn (k=1,2,3,4), produce a water dust Drop (y₁, μ_max), this process is repeated several times, the cloud cluster being made up of a large amount of water dusts that cloud reasoning device produces, calculate y₁ Average E (y₁) export as result.Wherein CG_Bk(k=1,2,3,4) 4 language of output variable are represented respectively The one-dimensional Y condition cloud generator that value is corresponding

Step d is by cellular automata and develops.By the cloud the reasoning results E (y of each cellular₁) and current time This cellular state value is added the state value obtaining subsequent time, thus generates the gray value matrix (unit of subsequent time Born of the same parents' state matrix).

Step e checks whether evolution result pattern meets user's requirement, is deposited into art pattern storehouse if meeting In, and proceed next step, if being unsatisfactory for being directly entered next step.

Step f judges whether evolution number of times reaches p time, if reaching, carries out fractal matrix iteration, if not reaching Develop to proceeding cloud model cellular automata.

The evolution result of step f is carried out fractal matrix iteration as generator matrix by step g, in order to obtain tool There is the fractal pattern of unlimited self-similarity.

Step g have employed fractal matrix iterative algorithm, specific as follows: order matrix A is as the life of iterated transform Become matrix, respectively with each element a of A_ij(1≤i≤m, 1≤j≤n) adds or is multiplied by (such as formula Shown in 1,2) matrix of each element gained of matrix A, removes substitutional element a_ijItself, produce matrix A ＇. A ＇ is the matrix of a local and global similarity, and its overall structure characteristic is identical with generator matrix.

$A^{\′}=A\⊕A=\left[\begin{array}{ccc}{a}_{11}+A& ....& a_{1n}+A\\ ....& ....& ....\\ a_{m1}+A& ....& a_{mn}+A\end{array}\right],$

Or

Step h judges whether total iterations reaches q time, if reaching, pattern generates process to be terminated, if not Reaching, pattern matrix step g obtained carries out cloud as the current state matrix of cloud model cellular automata Model element cellular automaton develops.

By regulating super entropy parameter, thus it is possible to vary the uncertain degree of details, to adapt to different design requirements, Especially when super entropy is 0, described method deteriorates to fractal fuzzy cellular automata method for generating pattern, now The pattern generated is uncertain without details, and the most fractal fuzzy cellular automata method for generating pattern is side of the present invention A kind of special case of method.

Experimental analysis:

In order to above advantage is described, experimental technique is used to be verified.First providing a resolution is 3 × 3 Initial pattern, its gray matrix is

$E=\left[\begin{array}{ccc}0& 255& 0\\ 255& 255& 255\\ 0& 255& 0\end{array}\right];$

Then relevant parameter is set: parameter p and q take 10 and 4 respectively, 3 X conditions of input language value The expected value Ex of cloud takes 255/4,510/4 and 765/4 respectively, and entropy En takes 255/12, output language value The expected value Ex of 4 Y condition clouds take-76.5 ,-21.5,21.5 and 76.5 respectively, entropy En takes 51/3.By arranging different super entropy He, if use the inventive method through 3 fractal matrix iterations and Dry time cellular develops the pattern that resolution is 81 × 81 obtained as shown in Fig. 3～11.

When super entropy He is not 0, such as Fig. 3～5 (He=En/400) and Fig. 6～8 (He=En/200) Shown in, although the pattern now generated also has fractal feature, but simultaneously again with the uncertainty of details, This is to have ambiguity and randomness due to cloud model simultaneously, and this uncertainty meets the incompleteness of pattern just Concept, namely relative with gestalt imperfect, if the pattern in Fig. 3, Fig. 4 is fractal on the whole, But be not full symmetric in details, this pattern often give people with new visual experience, and this The diversity planting details disclosure satisfy that people are to beautiful individual needs.Fig. 5 relatively Fig. 3, Fig. 4 are mixed and disorderly, and this is Due to along with the increase of evolution number of times, the randomness in cloud model is progressively amplified caused, additionally Fig. 6～8 points Not relatively Fig. 3～5 is mixed and disorderly, and reason is the randomness that the selection of super entropy can affect cloud model, super entropy is the biggest, Randomness is the strongest, then the pattern in detail uncertainty generated is the highest.So using the inventive method Generative Art Need during pattern to require that regulating super entropy size has the probabilistic complexity of details, drift to obtain according to design Bright and fractal pattern.When the super entropy of cloud model is set to 0, the inventive method deteriorates to fractal fuzzy unit Cellular automaton method for generating pattern, as shown in Fig. 9～11, it is possible to generate large amount of complex, beautiful and fractal Art pattern, but these patterns do not have the probabilistic feature of details.

Claims (1)

1. an artistic pattern forming method based on fractal cloud model cellular automata, is characterized in that, described method is to initialization Input picture after process carries out q fractal matrix iteration, and first carries out p cloud model unit before each fractal matrix iteration Cellular automaton develops, and generates a large amount of existing overall fractal effect, has again the probabilistic art pattern of details, described method bag Include following steps:

A. initialization processes:

Input picture is carried out pretreatment, picture is converted to gray-scale map and using the gray value matrix of gained pattern as at the beginning of cellular Beginning state matrix, then sets cloud model cellular automata evolution number of times p and fractal matrix iteration number of times q；

B. use selected cloud rule of inference that pattern gray value matrix is carried out cloud reasoning；

C. according to cloud the reasoning results, pattern gray value matrix is carried out anti-cloudization to process；

D. according to anti-cloud result, pattern gray value matrix is carried out cellular automata evolution:

By the cloud the reasoning results E (y of each cellular₁) state value obtaining subsequent time it is added with this cellular state value of current time, from And generate the gray value matrix of subsequent time；

E. being judged whether evolution result meets its requirement by user, being deposited into art pattern storehouse if meeting the requirements；

F. judging whether evolution number of times reaches p time, proceeding to step b if not, if proceeding to step g；

G. pattern gray value matrix step f obtained, as generator matrix, carries out fractal matrix iteration:

Order matrix A is as the generator matrix of iterated transform, respectively with each element a of A_ij(1≤i≤m, 1≤j≤n) adds Go up or be multiplied by the matrix of each element gained of matrix A, remove substitutional element a_ijItself, produce matrix A ＇

$A^{\′}=A\⊕A=\left[\begin{array}{ccc}{a}_{11}+A& \mathrm{...}& a_{1n}+A\\ \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{m1}+A& \mathrm{...}& a_{mn}+A\end{array}\right],$

Or

H. judge whether iterations reaches q time, proceed to step b if not and using A ＇ as new pattern gray value matrix, if It is to terminate；

In step b, input vector cloud specifically comprises the following steps that

Input vector cloud includes two input variables: the gray value x1 and neighborhood cellular average gray value x2 of center cellular, often Corresponding three kinds of sizing concept: the A of individual input variable₁={ grey level is low }, A₂={ grey level is medium }, A₃={ grey level is high }, Two input variables constitute input vector X；

Cloud for input vector is realized by two dimension X condition cloud generator, and two dimension X condition cloud generator is by one-dimensional X Condition cloud generator expands；For different systems, the shape of cloud is probably different, in view of the universality of Normal Cloud, Use Normal Cloud that variable is carried out cloud；The most corresponding 9 kinds of sizing concepts of input vector: { x1 Linguistic Value is A₁, x2 Linguistic Value is A₁, { x1 Linguistic Value is A₂, x2 Linguistic Value is A₁, { x1 Linguistic Value is A₃, x2 Linguistic Value is A₁, { x1 Linguistic Value is A₁, x2 Linguistic Value is A₂, { x1 Linguistic Value is A₂, x2 Linguistic Value is A₂, { x1 Linguistic Value is A₃, x2 Linguistic Value is A₂, { x1 Linguistic Value is A₁, x2 Linguistic Value is A₃, { x1 Linguistic Value is A₂, x2 Linguistic Value is A₃, { x1 Linguistic Value is A₃, X2 Linguistic Value is A₃, the corresponding two-dimentional X condition cloud generator of each Linguistic Value, each two dimension X condition cloud generator is by two Individual one-dimensional X condition cloud generator CG_AijConstitute with 1 multiplier MP, wherein represent input variable respectively when i=1,2,3 Linguistic Value is A₁、A₂And A₃, when j=1,2 time represent different input variables x1 and x2 respectively；First language of input vector { x1 Linguistic Value is A to speech value₁, x2 Linguistic Value is A₁Corresponding two-dimentional X condition cloud generator is by 2 one-dimensional X condition cloud generators CG_A11And CG_A12And 1 multiplier MP is constituted, CG_A11Represent the one-dimensional X condition that the 1st Linguistic Value of input variable x1 is corresponding Cloud generator, CG_A12Represent the one-dimensional X condition cloud generator that the 1st Linguistic Value of input variable x2 is corresponding, μ₁₁And μ₁₂Respectively For CG_A11And CG_A12Output degree of membership, μ₁₁And μ₁₂μ is obtained by multiplier MP₁=μ₁₁×μ₁₂, μ₁Represent and meet input The degree of membership of first Linguistic Value of vector, other 8 input vector Linguistic Value degrees of membership μ₂..., μ₉Calculating process and μ₁ Calculating process be similar to, the one-dimensional X condition cloud generator simply used is different；

Cloud rule of inference in step b is:

Described reasoning has output variable y₁, including 4 kinds of sizing concept: B₁={ small step degeneration }, B₂={ walking greatly degeneration }, B₃={ small step evolution }, B₄={ big stepping }, is respectively used to represent evolving and the degree degenerated of cellular；To any current time unit It is required to when born of the same parents make inferences meet following cloud rule of inference；Wherein, rule number is 9,9 kinds of languages of the most corresponding input vector Speech value；Degree of membership μ that input vector cloud obtains_m(m=1,2 ..., 9), represent the activation degree of the m article sizing rule respectively, Rule selector RS therefrom selects degree of membership μ of maximum_max, i.e. μ_maxCorresponding sizing rule is selected, according to cloud rule of inference Table selects corresponding output language value as the reasoning results；

In described step c, according to cloud the reasoning results, pattern gray value matrix is carried out anti-cloudization and process；

By μ_maxValue brings the one-dimensional Y condition cloud generator CG of corresponding output language value into_BkIn (k=1,2,3,4), produce a water dust Drop(y₁,μ_max), this process is repeated several times, the cloud cluster being made up of a large amount of water dusts that cloud reasoning device produces, calculate y₁Equal Value E (y₁) export as result；Wherein, CG_Bk(k=1,2,3,4) the one-dimensional Y that 4 Linguistic Values of output variable are corresponding is represented respectively Condition cloud generator；

Cellular automata evolutionary step in described step d is: by the cloud the reasoning results E (y of each cellular₁) and this yuan of current time Born of the same parents' state value is added the state value obtaining subsequent time, thus generates the gray value matrix of subsequent time；

Described step e being checked, whether evolution result pattern meets user's requirement, being deposited in art pattern storehouse if meeting, and Proceed next step, if being unsatisfactory for being directly entered next step；

The evolution result of step f is carried out fractal matrix iteration as generator matrix by described step g, it is thus achieved that have unlimited from The fractal pattern of similarity.