CN103177461A - Fractal cloud model cellular automation based art pattern generation method - Google Patents
Fractal cloud model cellular automation based art pattern generation method Download PDFInfo
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- CN103177461A CN103177461A CN2013100381687A CN201310038168A CN103177461A CN 103177461 A CN103177461 A CN 103177461A CN 2013100381687 A CN2013100381687 A CN 2013100381687A CN 201310038168 A CN201310038168 A CN 201310038168A CN 103177461 A CN103177461 A CN 103177461A
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Abstract
A fractal cloud model cellular automation based art pattern generation method is used for generating art patterns with existing integral fractal effect and detail uncertainty. According to the technical scheme, the method includes performing fractal matrix iteration for q times to an input picture subjected to initialization processing, and performing cloud model cellular automation evolution for p times before fractal matrix iteration each time to generate a large number of art patterns with existing integral fractal effect and detail uncertainty. Cloud model cellular automation is combined with a fractal matrix method, and fuzziness and randomness are taken into consideration in a pattern generation process, so that the generated art patterns are integrally fractals and have differences in detail to give a new visual perception to people, and personality needs of people on beauty can be met by the detail differences.
Description
Technical field
The present invention relates to a kind ofly can generate the fractal effect of existing integral body, have again the method for the uncertain art pattern of details, belong to technical field of data processing.
Background technology
The art pattern design is a kind of modeling activity take plane decoration as purpose, utilizes the fractal existing remarkable progress of art pattern design of carrying out, and Fractal Artistic Patterns has been subject to liking of people as a kind of art form.Appliance computer carries out Design of Fractal Artistic Patterns and depends on to a great extent the pattern generating algorithm, and these algorithms all are based upon on comprehensive utilization basis to composite principle and creation thought.At present basic Fractal Artistic Patterns generating algorithm mainly comprises two classes: a class is to adopt function iteration and based on the repeated application algorithm of aggregation process; Another kind of is to adopt tradition and fractal the algorithm composition technology that combines, composition as fractal in integral body and regular skeleton patterning process.Wherein whole fractal composition is according to certain algorithm model, the breadth of pattern to be carried out whole fractal structure, the picture that has infinite self-similarity characteristics with generation, fractal matrix is exactly the fractal patterning process of a kind of typical integral body, and it adopts the method for matrix iteration can access pure and fresh beautiful fractal pattern as a kind of simple pattern generating algorithm.But this method too relies on generator matrix, so the art pattern that adopts identical generator matrix to obtain is comparatively similar, is difficult to satisfy actual needs; Fuzzy cellular automata also is applied to art pattern and generates the field in addition, its dynamic behavior can produce various complexity, beautiful art pattern, the unpredictability of cellular automaton in the pattern generation process avoided in its constraint by fuzzy rule, makes cellular automaton develop to the direction of ideal pattern.The shortcoming of described method is only could produce the fractal pattern with infinite self-similarity characteristics when initial pattern is fractal pattern, and this has limited its range of application; The inventor once proposed a kind of fractal fuzzy cellular automata artistic pattern forming method, described method combines fractal matrix and fuzzy cellular automata method, adopting fuzzy cellular automata to carry out several times before the each iteration of fractal matrix develops, thereby make described method have the characteristics of the two kinds of methods in front concurrently, can generate complexity, beautiful and fractal art pattern.But, because described method is only considered the ambiguity that cellular automaton develops and is not considered randomness, the pattern that each evolution is produced be determine, full symmetric with gestalt.At present a kind of new art pattern mentality of designing is " whole fractal but on details, not exclusively symmetry or uncertain pattern tend to people with new visual experience ", characteristics in view of fractal fuzzy cellular automata method for generating pattern, it can't generate the fractal effect of this existing integral body and have again the probabilistic art pattern of details, so the art pattern that is difficult to satisfy under this mentality of designing generates needs, has also just limited its range of application.
Summary of the invention
The object of the invention is to the drawback for prior art, a kind of artistic pattern forming method based on fractal cloud model cellular automaton is provided, to generate the fractal effect of existing integral body, have again the uncertain art pattern of details.
Problem of the present invention realizes with following technical proposals:
A kind of artistic pattern forming method based on fractal cloud model cellular automaton, the input picture of described method after to initialization process carries out fractal matrix iteration q time, and first carried out p cloud model cellular automaton and develop before each fractal matrix iteration, generate the fractal effect of a large amount of existing integral body, have again the probabilistic art pattern of details, said method comprising the steps of:
A. initialization process:
The input picture is carried out pre-service, picture is converted to gray-scale map and with the gray-scale value matrix of the gained pattern original state matrix as cellular, then sets cloud model cellular automaton evolution number of times p and fractal matrix iteration number of times q;
B. adopt selected cloud inference rule to carry out the cloud reasoning to pattern gray-scale value matrix;
C. according to the cloud the reasoning results, pattern gray-scale value matrix is carried out anti-cloud processing;
D. according to anti-cloud result, pattern gray-scale value matrix is carried out cellular automaton develops:
Cloud the reasoning results E (y with each cellular
1) obtain next state value constantly with this cellular state value addition of current time, thus next gray-scale value matrix constantly generated;
E. judge by the user whether the evolution result meets its requirement, deposit it in the art pattern storehouse if meet the requirements;
F. judge whether the evolution number of times reaches p time, changes if not step b over to, if change step g over to;
G. the pattern gray-scale value matrix that step f is obtained carries out fractal matrix iteration as generator matrix:
Order matrix A uses respectively each element of A as the generator matrix of iterated transform
(1≤i≤m, 1≤j≤n) add or multiply by the matrix of each element gained of matrix A removes substitutional element
Itself produces matrix A ＇, wherein line number and the columns of m and n difference representing matrix
，
Or
H. judge whether iterations reaches q time, change if not step b over to and with A ＇ as new pattern gray-scale value matrix, if finish.
Above-mentioned artistic pattern forming method based on fractal cloud model cellular automaton is carrying out adopting Normal Cloud to carry out cloud to variable when the cloud model cellular automaton develops to picture.
The present invention combines the cloud model cellular automaton with fractal matrix method, consider simultaneously ambiguity and randomness in the pattern generative process, thereby the art pattern that makes generation is fractal on the whole, uncertain difference is arranged again on details, give new visual experience, the otherness of this details can satisfy people to the individual sexual demand of U.S..
Description of drawings
The invention will be further described below in conjunction with accompanying drawing.
Fig. 1 is the process flow diagram of technical solution of the present invention;
Fig. 2 is the cloud deduce machine that art pattern generates;
Fig. 3 be (
He=
En/ 400) after 3 iteration, 1 evolution art pattern generates result;
Fig. 4 be (
He=
En/ 400) after 3 iteration, 3 evolution art patterns generate results;
Fig. 5 be (
H=
En/ 400) after 3 iteration, 9 evolution art patterns generate results;
Fig. 6 be (
He=
En/ 200) after 3 iteration, 1 evolution art pattern generates result;
Fig. 7 be (
He=
En/ 200) after 3 iteration, 3 evolution art patterns generate results;
Fig. 8 be (
H=
En/ 200) after 3 iteration, 9 evolution art patterns generate results;
Fig. 9 be (
He=0) after 3 iteration, 1 evolution art pattern generates result;
Figure 10 be (
He=0) after 3 iteration, 3 evolution art patterns generate results;
Figure 11 be (
He=0) after 3 iteration, 9 evolution art patterns generate results.
In literary composition, symbol inventory used is: p is cloud model cellular automaton evolution number of times, and q is fractal matrix iteration number of times, and x1 and x2 are two input variables, and y1 is output variable,
Be the element of matrix A, μ represents degree of membership value, CG
AijAnd CG
BkBe cloud generator, MP is multiplier, and RS is the rules selection device.
Embodiment
Step a is pre-treatment step, the input picture is carried out pre-service, picture is converted to gray-scale map and obtains the gray-scale value matrix of pattern as the original state matrix of cellular, then determine correlation parameter, as cellular automaton evolution number of times p and fractal matrix iteration number of times q etc.
Step b, c, d all belong to the step that the cloud model cellular automaton develops.Here introducing purpose that the cloud model cellular automaton develops is to adopt the decision-making of cloud model reasoning simulation human brain to obtain desirable the have probabilistic complexity of details, beautiful and fractal pattern.
Step b, c have consisted of a complete cloud deduce machine jointly, and each cellular is carried out the cloud reasoning, and as shown in Figure 2, number of packages is 2 before this many conditions more rules deduce machine, regular number is 9, and concrete implementing method is as follows:
1) input vector cloud.Fig. 2 left-hand component is input vector cloud process, and this patent method comprises two input variables: the gray-scale value x1 of center cellular and neighborhood cellular average gray value x2, corresponding three kinds of qualitativing concepts (Linguistic Value): the A of each input variable
1={ grey level is low }, A
2={ grey level is medium }, A
3={ grey level is high }, two input variables have formed input vector X.Cloud for input vector realizes by two-dimentional X condition cloud generator, and two-dimentional X condition cloud generator is expanded by one dimension X condition cloud generator.For different systems, the shape of cloud may be different, and in view of the universality of Normal Cloud, this patent adopts Normal Cloud to carry out cloud to variable.Input vector is corresponding 9 kinds of typing concepts (Linguistic Value) altogether: { the x1 Linguistic Value is A
1, the x2 Linguistic Value is A
1, { the x1 Linguistic Value is A
2, the x2 Linguistic Value is A
1, { the x1 Linguistic Value is A
3, the x2 Linguistic Value is A
1, { the x1 Linguistic Value is A
1, the x2 Linguistic Value is A
2, { the x1 Linguistic Value is A
2, the x2 Linguistic Value is A
2}
,{ the x1 Linguistic Value is A
3, the x2 Linguistic Value is A
2, { the x1 Linguistic Value is A
1, the x2 Linguistic Value is A
3, { the x1 Linguistic Value is A
2, the x2 Linguistic Value is A
3, { the x1 Linguistic Value is A
3, the x2 Linguistic Value is A
3, the corresponding two-dimentional X condition cloud generator of each Linguistic Value, each two-dimentional X condition cloud generator is by two one dimension X condition cloud generator CG
AijConsist of with 1 multiplier MP, wherein as i=1,2, represent that respectively the input variable Linguistic Value is A 3 the time
1, A
2And A
3, represent respectively different input variable x1 and x2 as j=1,2 the time.For example, { the x1 Linguistic Value is A to first Linguistic Value of input vector
1, the x2 Linguistic Value is A
1Corresponding two-dimentional X condition cloud generator is by 2 one dimension X condition cloud generator CG
A11And CG
A12And 1 multiplier MP formation, CG
A11One dimension X condition cloud generator corresponding to expression the 1st Linguistic Value of input variable x1, CG
A12One dimension X condition cloud generator corresponding to expression the 1st Linguistic Value of input variable x2, μ
11And μ
12Be respectively CG
A11And CG
A12The output degree of membership, μ
11And μ
12MP obtains μ by multiplier
1=μ
11* μ
12, μ
1The degree of membership of first Linguistic Value of input vector is satisfied in expression.Other 8 input vector Linguistic Value degree of membership μ
2..., μ
9Computation process and μ
1Computation process similar, the one dimension X condition cloud generator that just adopts is different.
2) cloud inference rule.This reasoning has an output variable y1, and it comprises 4 kinds of qualitativing concepts (Linguistic Value): B
1={ small step degeneration }, B
2={ the large step degenerates }, B
3={ small step evolution }, B
4={ large stepping } is respectively used to represent the degree of evolution and the degeneration of cellular.All require to meet following cloud inference rule when any current time cellular is carried out reasoning, as shown in table 1, regular number is 9, respectively 9 kinds of Linguistic Values of corresponding input vector.
The cloud inference rule that table 1 art pattern generates
3) cloud reasoning.Fig. 2 center section is the cloud reasoning process, the degree of membership μ that the input vector cloud obtains
m(m=1,2 ..., 9), represent that respectively the activation degree of m bar qualitative rule, rules selection device RS therefrom select maximum degree of membership μ
max, i.e. μ
maxCorresponding qualitative rule is selected, selects corresponding output language value as the reasoning results according to cloud inference rule table.
4) anti-cloud output.Fig. 2 right-hand component is anti-cloud output procedure, with μ
maxValue is brought the one dimension Y condition cloud generator CG of corresponding output language value into
BkIn (k=1,2,3,4), produce a water dust Drop (y
1, μ
max), repeatedly repeat this process, the cloud cluster that is formed by a large amount of water dusts that the cloud deduce machine produces, calculating y
1Average E (y
1) as a result of output.CG wherein
Bk(k=1,2,3,4) represent respectively the one dimension Y condition cloud generator that 4 Linguistic Values of output variable are corresponding
Steps d is to carry out cellular automaton to develop.Cloud the reasoning results E (y with each cellular
1) obtain next state value constantly with this cellular state value addition of current time, thus next gray-scale value matrix (cellular state matrix) constantly generated.
Step e check evolution as a result pattern whether satisfy customer requirements, if satisfy, it is deposited in the art pattern storehouse, and proceeds next step, directly do not enter next step if do not satisfy.
Step f judges whether the evolution number of times reaches p time, carries out fractal matrix iteration if reach, and does not proceed the evolution of cloud model cellular automaton if reach.
Step g is carried out fractal matrix iteration with the evolution result of step f as generator matrix, in order to obtain to have the fractal pattern of unlimited self-similarity.
Step g has adopted fractal matrix iterative algorithm, and is specific as follows: order matrix A uses respectively each element of A as the generator matrix of iterated transform
(1≤i≤m, the matrix of each element gained of 1≤j≤n) add or multiply by (shown in formula 1,2) matrix A removes substitutional element
Itself produces matrix A ＇.A ＇ is the matrix of a part and global similarity, and its one-piece construction characteristic is identical with generator matrix.
（2）
Step h judges whether total iterations reaches q time, finishes if reach the pattern generative process, does not carry out the cloud model cellular automaton as the current state matrix of cloud model cellular automaton and develops if reach the pattern matrix that step g obtained.
By regulating super entropy parameter, can change the uncertain degree of details, to adapt to different designing requirements, especially when super entropy is 0, described method deteriorates to fractal fuzzy cellular automata method for generating pattern, the pattern that generate this moment is uncertain without details, and namely fractal fuzzy cellular automata method for generating pattern is a kind of special case of the inventive method.
Experimental analysis:
For above advantage is described, adopt the experimental technique proved.Resolution of given first is 3 * 3 initial pattern, and its gray matrix is E=
Then correlation parameter is set: parameter p and q get respectively 10 and 4, the expectation value Ex of 3 X condition clouds of input language value gets respectively 255/4,510/4 and 765/4, entropy En gets 255/12, the expectation value Ex of 4 Y condition clouds of output language value gets respectively-76.5 ,-21.5,21.5 and 76.5, and entropy En gets 51/3.By different super entropy He is set, adopting this patent method is that 81 * 81 pattern is as shown in Fig. 3～11 through the develop resolution that obtains of 3 fractal matrix iterations and several times cellular.
when super entropy He is not 0, as shown in Fig. 3～5(He=En/400) and Fig. 6～8(He=En/200), although the pattern that generate this moment also has fractal characteristics, but simultaneously again with the uncertainty of details, this is because cloud model has ambiguity and randomness simultaneously, this uncertainty meets the incomplete concept of pattern just, namely relative with gestalt imperfect, as Fig. 3, pattern in Fig. 4 is fractal on the whole, but be not full symmetric on details, this pattern tends to people with new visual experience, and the otherness of this details can satisfy people to the individual sexual demand of U.S..Fig. 5 is mixed and disorderly than Fig. 3, Fig. 4, this is due to the increase along with the evolution number of times, due to randomness in cloud model is amplified gradually, Fig. 6～8 are mixed and disorderly than Fig. 3～5 respectively in addition, reason is the randomness that the selection of super entropy can affect cloud model, super entropy is larger, randomness is stronger, and the pattern in detail uncertainty that generates is higher.Have the probabilistic complexity of details, beautiful and fractal pattern so need to regulate super entropy size according to designing requirement when adopting this patent method Generative Art pattern with acquisition.When the super entropy of cloud model is made as 0, the this patent method deteriorates to fractal fuzzy cellular automata method for generating pattern, as shown in Fig. 9～11, can generate large amount of complex, beautiful and fractal art pattern, but these patterns do not have the probabilistic feature of details.
Claims (2)
1. artistic pattern forming method based on fractal cloud model cellular automaton, it is characterized in that, the input picture of described method after to initialization process carries out fractal matrix iteration q time, and first carried out p cloud model cellular automaton and develop before each fractal matrix iteration, generate the fractal effect of a large amount of existing integral body, have again the probabilistic art pattern of details, said method comprising the steps of:
A. initialization process:
The input picture is carried out pre-service, picture is converted to gray-scale map and with the gray-scale value matrix of the gained pattern original state matrix as cellular, then sets cloud model cellular automaton evolution number of times p and fractal matrix iteration number of times q;
B. adopt selected cloud inference rule to carry out the cloud reasoning to pattern gray-scale value matrix;
C. according to the cloud the reasoning results, pattern gray-scale value matrix is carried out anti-cloud processing;
D. according to anti-cloud result, pattern gray-scale value matrix is carried out cellular automaton develops:
Cloud the reasoning results E (y with each cellular
1) obtain next state value constantly with this cellular state value addition of current time, thus next gray-scale value matrix constantly generated;
E. judge by the user whether the evolution result meets its requirement, deposit it in the art pattern storehouse if meet the requirements;
F. judge whether the evolution number of times reaches p time, changes if not step b over to, if change step g over to;
G. the pattern gray-scale value matrix that step f is obtained carries out fractal matrix iteration as generator matrix:
Order matrix A uses respectively each element of A as the generator matrix of iterated transform
(1≤i≤m, 1≤j≤n) add or multiply by the matrix of each element gained of matrix A removes substitutional element
Itself produces matrix A ＇
Or
H. judge whether iterations reaches q time, change if not step b over to and with A ＇ as new pattern gray-scale value matrix, if finish.
2. a kind of artistic pattern forming method based on fractal cloud model cellular automaton according to claim 1, is characterized in that, picture carried out adopt Normal Cloud to carry out cloud to variable when the cloud model cellular automaton develops.
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| TWI717797B (en) * | 2019-08-05 | 2021-02-01 | 曹文峰 | Totem forming system, method, equipment, product and computer readable storage device |
| CN113160413A (en) * | 2021-02-25 | 2021-07-23 | 北京大学 | Real-time dynamic cloud layer drawing method based on cellular automaton |
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| CN102254105A (en) * | 2011-08-10 | 2011-11-23 | 武汉大学 | Urban sprawl forecasting method based on cloud model cellular automata |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| TWI717797B (en) * | 2019-08-05 | 2021-02-01 | 曹文峰 | Totem forming system, method, equipment, product and computer readable storage device |
| CN113160413A (en) * | 2021-02-25 | 2021-07-23 | 北京大学 | Real-time dynamic cloud layer drawing method based on cellular automaton |
| CN113160413B (en) * | 2021-02-25 | 2022-07-12 | 北京大学 | Real-time dynamic cloud layer drawing method based on cellular automaton |
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