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一维元胞自动机模型的精确解
Exact Solution of One-Dimensional Cellular Automata Model

DOI: 10.12677/CSA.2021.117196, PP. 1915-1922

Keywords: 元胞,元胞自动机,模型,关联函数,精确解
Cellular
, Cellular Automaton, Model, Correlation Function, Exact Solution

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Abstract:

研究一维元胞自动机模型,求出一维元胞自动机模型的精确解,讨论元胞能量T不同的情况下,所有元胞的状态是馄饨的到所有元胞的状态是相同的性质的强度M随着元胞间相互作用的动力B变化的关系可以看出,对于一切 T > 0 (即外界对元胞所提供的能量大于元胞所耗损的能量)的时候都有M(T,0)=0。这表明在一维的情况下,CA模型不能够通过近邻格点间的相互通信使得各元胞之间的轨迹在一定空间范围内能够呈现出有序排列而获得能够被相互作用的性质,所以无论元胞的能量是多少,格点的平均取向是由两个对抗的因素相互竞争而决定的,即能量倾向于取极小,而熵倾向于取极大,对于一维CA模型情况来讲,由于近邻数比较低,使得格点排在相同方向的倾向不足以抗衡使得熵极大的倾向。
The exact solution of the one-dimensional cellular automata model is obtained by studying the one-dimensional cellular automata model. When the cellular energy T is different, the relationship between the strength M of all cells which are wonton and the state of all cells is the same property changes with the dynamic force B of the interaction between the cells can be seen M(T,0)=0. ? when T > 0 (that is, the energy produced by cells is greater than the energy consumed by cells). This shows that in one-dimensional case, CA model can’t make the tracks among the cells which show an orderly arrangement in a certain spatial range and get the property of interaction. Therefore, no matter what the energy of the cells is, the average orientation of the cells is determined by two competing factors, that is, the energy tends to be minimal, while the entropy tends to be maximal. For one-dimensional CA model, due to the low number of neighbors, the tendency of the cells to be arranged in the same direction is insufficient.

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