Method for identifying emergence phenomenon
By designing a cell-like automaton model and using the Pearson correlation coefficient and emergence index E, the problem of judging whether order will emerge during the evolution of cellular automatons is solved, and effective judgment of emergence boundaries and model parameters are achieved.
Patent Information
- Application Number
- CN202411771564.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-04
- Publication Date
- 2025-03-28
AI Technical Summary
The prior art is difficult to judge whether order will emerge during the evolution of cellular automatons through model parameters, and the critical point of the 'chaotic edge' is controversial.
A cell-like automata model is designed, and two-dimensional cell-like automata is constructed through different neighborhood models and local rule functions. The Pearson correlation coefficient is used as an evaluation index to construct the emergence index E to judge whether it can emerge and divide the emergence boundary.
It is realized that the model parameters are used to determine whether order will emerge during the evolution of cell-like automatons, and the concept of emergence of boundaries is proposed, indicating that the E-values that can be produced in the same neighborhood range have boundaries, and the E-values that can be produced in different neighborhood ranges have differences.
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Figure CN119721268A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of cellular automata, and in particular to a method for identifying emergence phenomena. Background Art
[0002] Since the concept of emergence was proposed, many scholars have conducted verification research in many fields such as nature, human society, and artificial systems. It is expected to become a new paradigm of holism, but there is still no recognized scientific definition to summarize the ubiquitous emergence phenomenon. Previous studies have summarized three characteristics of emergence: First, from a macro perspective, the emergent characteristics are not the sum of their micro characteristics; second, from the perspective of novelty, the types of emergent characteristics are completely different from the types of individual characteristics; third, from the perspective of dynamics, the emergent characteristics cannot be deduced or predicted from the behavior of independent individuals.
[0003] To further study the emergence phenomenon, scholars have explored emergence by observing natural phenomena and building models. These are formed by the interaction of multiple simple agents under simple rules, such as cellular automata, artificial neural networks, artificial life models, genetic algorithms, ant colony algorithms, bee colony algorithms, artificial immune algorithms, etc. The literature [Langton CG. Computation at the edge of chaos: Phase transitions and emergent computation [J], Physica D, 1990, 42 (1): 12-27.] believes that there is a boundary between chaos and order in the evolution of the system, namely the "edge of chaos". At present, Langton parameters, evolutionary entropy, topological entropy and other methods have been used to analyze the complex evolutionary behavior of cellular automata, but the critical point of the "edge of chaos" in the evolution of cellular space is still controversial.
[0004] Under the same rule parameters, there is a transition between chaos and order in the cellular space during the evolution of cellular automata. Is there a model in which only chaos exists or order emerges during the evolution after the parameters are set? Can we judge whether the model can emerge during the evolution by the model parameters? Based on this, the present invention proposes a method for identifying the emergence phenomenon, and explores and proposes the concept of emergence boundary. Summary of the invention
[0005] The present invention aims to provide a method for identifying emergence phenomena, so as to determine whether emergence can occur during the evolution of the model through model parameters, and to explore and propose the concept of emergence boundary.
[0006] In order to achieve the above object, the present invention provides the following technical solutions:
[0007] A method for identifying an emergence phenomenon comprises the following steps:
[0008] S1. Design a quasi-cellular automaton whose evolution process only shows two states: chaos or order. It can be expressed in mathematical symbols as follows:
[0009] A=(L,d,S,N,f)
[0010] Among them, L is the cellular space, d is the dimension of the cellular space in the cellular automaton, S is the finite and discrete state set of the cell, N is the set of all cellular states in a neighborhood, and f is the local rule;
[0011] S2. Use different neighborhood models to construct two-dimensional cellular automata and perform evolution;
[0012] S3. Use the Pearson correlation coefficient as an evaluation index to determine whether the cellular space emerges during the evolution of the cellular automation. The formula is:
[0013]
[0014] The random variables x and y represent two adjacent rows or columns in the cell space of the quasi-cellular automaton at a certain moment, and n is the number of variables involved in the operation;
[0015] S4. Analyze the Pearson correlation coefficient of quasi-cellular automata of different neighborhood models under different cell state sets and different local rules;
[0016] S5. Comprehensively analyze the evolution process of cellular automata, construct the emergence index E to evaluate whether cellular automata can emerge, and divide the emergence boundary according to the emergence index E.
[0017] Furthermore, in step S1, the operation rules of the quasi-cellular automaton are as follows: it is defined that each cell in the initial cell space L is generated by a random function. In the subsequent evolution process, the cell value is jointly determined by the cell neighborhood N and the local rule function at the previous moment. When the cell neighborhood N meets the local rule function f, the cell value is determined. When the cell neighborhood N does not meet the requirements of the local rule function f, the cell value continues to be generated by the random function.
[0018] Further, in step S2, the neighborhood model includes Moore neighborhood, von Neumann neighborhood and Margolus neighborhood.
[0019] Furthermore, in step S2, a two-dimensional quasi-cellular automaton constructed with a Moore-type neighborhood is defined, and the values of all cells in the 100×100 cell space L are defined as 0 or 1, that is, the cell state set S={0,1}. The initial value of each cell is determined by a random function, and then the local rule function f(4) is defined according to the herd principle: let n0 be the number of 8 cells with values 0 around the Moore-type neighborhood N of the central cell, and n1 be the number of 8 cells with values 1 around it. When n0 is greater than 4, the value of the central cell at the next moment is 0, and when n1 is greater than 4, the value of the central cell at the next moment is 1. If the condition is not met, the value of the central cell at the next moment continues to be randomly generated; by analogy, f(5) indicates that when the number of identical cells in the neighborhood is greater than 5, the value of the central cell is determined, and f(6) indicates that when the number of identical cells in the neighborhood is greater than 6, the value of the central cell is determined.
[0020] Furthermore, in step S5, let n represent the number of cells participating in the calculation in the cellular automaton-like neighborhood model, s be the number of cell state sets in the cellular automaton-like neighborhood model, and p be the probability of satisfying the local rule function in the neighborhood model. The constructor is as follows:
[0021] E=n×e s ×p.
[0023] The principle and beneficial effects of this technical solution:
[0024] The present invention proposes a cellular automaton model, and uses correlation analysis to determine whether the cellular space of the cellular automaton produces emergence. Under different conditions such as cell state sets, neighborhood ranges, and local rule functions, the evolution of the cellular automaton presents two results, one is chaos and disorder, and the other is order. Based on this, the concept of emergence boundary is proposed. The emergence index E is introduced to determine whether the cellular automaton can emerge. The results show that there is a boundary for the E value that can produce emergence in the same neighborhood range, and there are differences in the boundaries of the E values that can emerge in different neighborhood ranges. BRIEF DESCRIPTION OF THE DRAWINGS
[0025] Figure 1 It is a Moore-type neighborhood model;
[0026] Figure 2 Some results of the evolution of Moore-type cellular automata;
[0027] Figure 3 The average value of the correlation coefficient of adjacent rows in the cellular space during the evolution process and the visualization diagram of the cellular space when the evolution step is 500;
[0028] Figure 4 is the average value of the correlation coefficient of adjacent rows in the evolution process of different Moore-type cellular automata;
[0029] Figure 5It is a scatter plot comparing the average values of correlation coefficients of adjacent rows in the evolution process of Moore-type cellular automation under the same conditions;
[0030] Figure 6 It is a von Neumann type and Margolus type neighborhood model. DETAILED DESCRIPTION
[0031] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:
[0032] A method for identifying an emergence phenomenon comprises the following steps:
[0033] S1. Design a quasi-cellular automaton whose evolution process only shows two states: chaos or order. It can be expressed in mathematical symbols as follows:
[0034] A=(L,d,S,N,f)
[0035] Among them, L is the cellular space, d is the dimension of the cellular space in the cellular automaton, S is the finite and discrete state set of the cell, N is the set of all cells in a neighborhood, and f is the local rule.
[0036] The mathematical elements of quasi-cellular automata are the same as those of cellular automata, both of which are composed of cellular space, cellular state set, neighborhood model and state update rules, but their operation rules are completely different from those of cellular automata. The rules are as follows: each cell in the initial cellular space L is defined to be generated by a random function. In the subsequent evolution process, the cell value is jointly determined by the cell neighborhood N and the local rule function at the previous moment. When the cell neighborhood N meets the local rule function f, the cell value is determined. When the cell neighborhood N does not meet the requirements of the local rule function f, the cell value continues to be generated by the random function.
[0037] S2. Use different neighborhood models to construct two-dimensional cellular automata and evolve them.
[0038] This embodiment uses Moore-type neighborhood to construct a two-dimensional cellular automaton. Moore-type neighborhood is a common neighborhood model of two-dimensional cellular automaton, which includes 9 grids with a radius r=1 and a cell as the center. Figure 1 shown.
[0039] A two-dimensional quasi-cellular automaton is constructed with a Moore-type neighborhood, and the values of all cells in the 100×100 cell space L are defined as 0 or 1, that is, the cell state set S = {0,1}. The initial value of each cell is generated by a random function, and the result is as follows Figure 2(a) is shown. The local rule function f(4) is defined according to the herd principle: let n0 be the number of 8 cell values around the Moore-type neighborhood N of the central cell with a value of 0, and n1 be the number of 8 surrounding cell values with a value of 1. When n0 is greater than 4, the value of the central cell at the next moment is 0, and when n1 is greater than 4, the value of the central cell at the next moment is 1. If the condition is not met, the value of the central cell at the next moment continues to be randomly generated. Similarly, f(5) means that when the number of identical cells in the neighborhood is greater than 5, the value of the central cell is determined, and f(6) means that when the number of identical cells in the neighborhood is greater than 6, the value of the central cell is determined. In the evolution process, with the surrounding cellular space as fixed boundaries, the local rule function starts from the upper left corner, and traverses each neighborhood center in the cellular space from left to right and from top to bottom until it ends at the lower right corner, completing an evolution. All evolutions in the present invention adopt this same order.
[0040] Depend on Figure 2 (a) It can be seen that when the step length is t = 1, the initially randomly generated cellular space is disordered. After the first evolution (t = 2), discrete small patches appear in the cellular space, such as Figure 2 (b) After the fourth evolution (t = 5), an orderly and continuous pattern appears in the cellular space, such as Figure 2 (c).
[0041] The pattern is the fundamental characteristic of the emergence of complex systems. The pattern in the cellular space at different time and space scales is the basis for judging whether the cellular space has emerged. From the evolution process of quasi-cellular automata, there is no additivity between adjacent steps, and there is nonlinearity between cellular spaces of different steps. The evolution process is not deducible. The large patches in the evolved cellular space are features that the original cellular space does not have, and they are novel. Under the action of the local rule function f, the quasi-cellular automata evolve from disorder to order, produce self-organization phenomena, and meet the three characteristics of emergence.
[0042] S3. Use the Pearson correlation coefficient as an indicator to determine whether the cellular space emerges during the evolution of the quasi-cellular automation. The formula is:
[0043]
[0044] The random variables x and y represent two adjacent rows or columns in the cellular space of the quasi-cellular automaton at a certain moment, and n is the number of variables involved in the operation.
[0045] After the emergence of quasi-cellular automata, the cells in the cellular space have high autocorrelation. The Pearson correlation analysis method is introduced as an indicator to judge whether the cellular space emerges during the evolution of quasi-cellular automata. The Pearson correlation coefficient between two variables is defined as the covariance of the two variables x and y divided by the product of their standard deviations.
[0046] When the cells in the cellular space are disordered, the correlation coefficient between the values of two adjacent rows of cells is low. When a pattern appears in the cellular space, the correlation coefficient between the values of two adjacent rows of cells is high. Figure 3 As shown, Figure 3 The red dot in the middle is the average value of the correlation coefficient between two adjacent rows in each cellular space during the evolution of the quasi-cellular automaton with emergence phenomenon. The upper right figure is the visualization result of the cellular space when the evolution step length is t=500. Figure 3 The blue dot in the middle is the average value of the correlation coefficient between two adjacent rows in each cellular space during the evolution of the cellular automaton without emergence. The lower right figure is the visualization result of the cellular space when the evolution step is t = 500. When emergence occurs during the evolution of the cellular automaton, the originally discrete and disordered cellular space appears to have continuous and orderly patterns, and the cell values of two adjacent rows evolve from being unrelated to having a certain correlation, or even highly correlated. Therefore, the average value of the correlation coefficient value of two adjacent rows changes greatly, which can be used as an indicator to judge whether emergence occurs during the evolution of the cellular automaton.
[0047] S4. Analyze the Pearson correlation coefficient of quasi-cellular automata in different neighborhoods under different cell sets and different local rules.
[0048] (1) Moore-type cellular automata under different cell state sets and different local rule functions
[0049] Taking a 100×100 two-dimensional cellular space as an example, the cellular state set and local rule function of the Moore-type cellular automaton are changed in sequence. During the evolution process, the average value of the correlation coefficient between two adjacent rows of the cellular space is as follows: Figure 4 As shown. The local rule function is gradually improved from f(4) (when the number of identical cell values in the Moore-type neighborhood at time t is greater than 4, the central cell value at time t+1 is determined, otherwise the central cell value is randomly generated) to f(6) (when the number of identical cell values in the Moore-type neighborhood at time t is greater than 6, the central cell value at time t+1 is determined, otherwise the central cell value is randomly generated), and the evolution of the three local rule functions in the five cellular spaces of the cellular state set S1 = {0,1}, S2 = {0,1,2}, S3 = {0,1,2,3}, S4 = {0,1,2,3,4} and S5 = {0,1,2,3,4,5} is compared. By Figure 4 (a) It can be seen that when the local rule function is f(4), only the cell state set S5 does not have emergence phenomenon, and the smaller the number of cell state sets, the earlier the emergence occurs. Figure 4 (b) It can be seen that when the local rule function is f(5), only the cell state set S1 appears to emerge. Figure 4 (c) It can be seen that when the local rule function is f(6), none of the five cell state sets show emergence.
[0050] Figure 5 The figure is a scatter plot comparing the average values of the correlation coefficients of adjacent rows of the same step length in the cell space during multiple evolutions of the Moore-type cellular automaton under the same conditions. In different times of evolution, the initial state of the cellular automaton is randomly generated. Figure 5 (a) is a comparison of the evolution of two Moore-type cellular automata with a cell state set of S1 = {0, 1} and a local rule function of f(4). The same cellular automata evolution process is repeated many times, and the average absolute value of the correlation coefficient of adjacent rows in the cell space of different evolution processes is R 2 is above 0.95, and the emergence time of the cellular space is close, such as Figure 5 This shows that whether the cellular space emerges during the evolution of quasi-cellular automata has nothing to do with the initial conditions.
[0051] (2) Evolution of other neighborhood models of cellular automata
[0052] Moore's neighborhood is just one common neighborhood model in two-dimensional cellular automata. Other common neighborhood models include von Neumann and Margolus, which are defined as follows: Figure 6 Taking the 100×100 two-dimensional cellular space as an example, the neighborhood model, cellular state set and local rule function of the cellular automaton are changed in turn, and the Pearson correlation analysis method is used to detect the average correlation coefficient of adjacent rows in each cellular space, and the evolution of the von Neumann type and Margolus type cellular automaton under different conditions is obtained, as shown in Table 1.
[0053] As shown in Table 1, the emergence phenomenon only occurs in the cellular space of the von Neumann-type cellular automaton when the local rule function is f(2), and the cellular state sets S1 = {0,1}, S2 = {0,1,2}, and S3 = {0,1,2,3}. For the Margolese-type cellular automaton, when the cellular state set S1 = {0,1}, the local rule functions f(12) to f(17) can all cause the emergence phenomenon in the cellular space. When the cellular state set S2 = {0,1,2}, the local rule functions f(12) to f(14) can cause the emergence phenomenon in the cellular space. When the cellular state set S3 = {0,1,2,3}, only the local rule function f(12) can cause the emergence phenomenon in the cellular space.
[0054] Table 1 The emergence of von Neumann-type and Margolis-type cellular automata under different conditions
[0055]
[0056] S5. Comprehensively analyze the evolution process of cellular automata, construct the emergence index E to evaluate whether cellular automata can emerge, and divide the emergence boundary according to the emergence index E.
[0057] Comprehensively analyze the cellular automaton evolution process of three neighborhood models, such as Figure 4 From Table 1, we can see that there are boundary conditions for the emergence of cellular automata in the neighborhood model. The emergence index E of cellular automata is proposed to evaluate whether cellular automata can emerge. Let n represent the number of cells participating in the calculation in the neighborhood model of cellular automata, s be the number of cell state sets in the cellular automata, and p be the probability of satisfying the local rule function in the neighborhood model. The constructor is as follows:
[0058] E=n×e s ×p
[0059] According to the above formula, the E values of cellular automata of different neighborhood models under different conditions are calculated, and the results are shown in Table 2. The underlined E values of cellular automata without emergence in Table 2 are shown. From Table 2, it can be seen that the von Neumann type cellular automata have emergence when the E value is between 18 and 45, the Moore type has emergence when the E value is between 17 and 62, and the Margolus type has emergence when the E value is greater than 4.
[0060] Table 2 E values of different neighborhood types of cellular automata under different conditions
[0061]
[0062]
[0063] The initial state of the cellular space of the cellular automaton is random and disordered. Under different neighborhood models and model parameters, some cellular spaces emerge with order and form ordered patterns, while others cannot emerge with order. At any time, the cellular space remains in a chaotic and disordered state. The emergence boundary is defined according to the emergence index to distinguish whether the evolution of the cellular automaton can produce emergence. Compared with the edge of chaos, the edge of chaos is used to describe the boundary between chaos and emergence in the process of model evolution, while the emergence boundary is used to distinguish whether the model can produce emergence under different parameters.
[0064] The present invention proposes a cellular automaton model to explore the emergence boundary, takes the average correlation coefficient of adjacent rows in the cellular space as the emergence index of the cellular space, evaluates whether the cellular space generates emergence, and constructs a function to calculate the emergence index of the cellular automaton to measure whether the cellular automaton can generate emergence during the evolution process. The concept of emergence boundary is proposed. When the model parameters meet the emergence requirements, the model will generate emergence phenomena during the evolution process. When the model parameters do not meet the emergence requirements, the model will remain chaotic and disordered during the evolution process.
[0065] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions and / or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.
Claims
1. A method for identifying an emergent phenomenon, characterized in that: The steps include: S1. Design a quasi-cellular automaton whose evolution process only shows two states: chaos or order. It can be expressed in mathematical symbols as follows: A=(L,d,S,N,f) Among them, L is the cellular space, d is the dimension of the cellular space in the cellular automaton, S is the finite and discrete state set of the cell, N is the set of all cellular states in a neighborhood, and f is the local rule; S2. Use different neighborhood models to construct two-dimensional cellular automata and perform evolution; S3. Use the Pearson correlation coefficient as an evaluation index to determine whether the cellular space emerges during the evolution of the cellular automation. The formula is: The random variables x and y represent two adjacent rows or columns in the cell space of the quasi-cellular automaton at a certain moment, and n is the number of variables involved in the operation; S4. Analyze the Pearson correlation coefficient of quasi-cellular automata of different neighborhood models under different cell state sets and different local rules; S5. Comprehensively analyze the evolution process of cellular automata, construct the emergence index E to evaluate whether cellular automata can emerge, and divide the emergence boundary according to the emergence index E.
2. The method for identifying an emergence phenomenon according to claim 1, characterized in that: In step S1, the operation rules of the quasi-cellular automaton are as follows: define that each cell in the initial cell space L is generated by a random function. In the subsequent evolution process, the cell value is jointly determined by the cell neighborhood N and the local rule function at the previous moment. When the cell neighborhood N meets the local rule function f, the cell value is determined. When the cell neighborhood N does not meet the requirements of the local rule function f, the cell value continues to be generated by the random function.
3. The method for identifying an emergence phenomenon according to claim 1, characterized in that: In step S2, the neighborhood model includes Moore neighborhood, von Neumann neighborhood and Margolus neighborhood.
4. The method for identifying an emergence phenomenon according to claim 3, characterized in that: In step S2, a two-dimensional quasi-cellular automaton constructed with a Moore-type neighborhood is defined, and the values of all cells in the 100×100 cell space L are defined as 0 or 1, that is, the cell state set S={0,1}. The initial value of each cell is determined by a random function, and then the local rule function f(4) is defined according to the herd principle: let n0 be the number of 8 cells with values 0 around the Moore-type neighborhood N of the central cell, and n1 be the number of 8 cells with values 1 around it. When n0 is greater than 4, the value of the central cell at the next moment is 0, and when n1 is greater than 4, the value of the central cell at the next moment is 1. If the condition is not met, the value of the central cell at the next moment continues to be randomly generated; by analogy, f(5) indicates that when the number of identical cells in the neighborhood is greater than 5, the value of the central cell is determined, and f(6) indicates that when the number of identical cells in the neighborhood is greater than 6, the value of the central cell is determined.
5. The method for identifying an emergence phenomenon according to claim 1, characterized in that: In step S5, let n represent the number of cells participating in the calculation in the cellular automaton-like neighborhood model, s represent the number of cell state sets in the cellular automaton-like neighborhood model, and p represent the probability of satisfying the local rule function in the neighborhood model. The constructor is as follows: E=n×e s ×p。