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元胞自动机-如何处理边界细胞？

[英]Cellular automata - what to do on boundary cell?

原文 2015-12-13 14:24:27 0 1 java/ cellular-automata

I'm trying to implement a cellular automata simulating wave behaviour. 我正在尝试实现模拟波行为的元胞自动机。 I'm using Von Neumann neighbourhood with r=2 like here 我正在使用r=2 Von Neumann社区，如下所示

My question is: How should I count state of the cell on the boundary? 我的问题是：如何计算边界上单元的状态？

For example: I'm having an array a , and I want to count value of a[0][0] . 例如：我有一个数组a ，我想计算a[0][0] 。

States of cells are floats in range of (-1,1) where 0 is land. 单元格的状态是（-1,1）范围内的浮点数，其中0是陆地。 On "regular" cells I can take states of neighbours, but when there are fewer neighbours (<12) the result is just wrong, and "generates" a new wave. 在“常规”单元上，我可以采用邻居状态，但是当邻居较少（<12）时，结果就是错误的，并“产生”了新的浪潮。

1 个解决方案

There are different solutions to your problem. 您的问题有不同的解决方案。

Periodic boundary condition : consider the lattice as a torus and use a modulo to loop your cells. 周期性边界条件：将晶格视为圆环，并使用模来循环您的单元格。

Example: a[-1][0] = a[n-2][0] 例如：a [-1] [0] = a [n-2] [0]

Good side: this avoid any "border-effect" by making the lattice invariant by translation, which should lead to a more natural evolution. 好的一面：通过平移晶格使其不变，可以避免任何“边界效应”，这应该导致更自然的进化。 Bad side: at smaller scales, this can have undesired effects such as resonance. 不好的一面：在较小的范围内，这可能会产生不良影响，例如共振。

This approach is particularly suitable if you wanna do a quantitative study of your model, such as phase transition, mean-field, etc.. 如果您想对模型进行定量研究，例如相变，均场等，则此方法特别适合。

Inert boundary condition : consider the border of your lattice to have an absorbing rule, that is, they simulate "external" cells which always have the same inert states. 惰性边界条件：考虑晶格的边界具有吸收规则，也就是说，它们模拟始终具有相同惰性状态的“外部”单元。

Example: a[-1][0] = 10e-6 or so because 0 means land. 示例：a [-1] [0] = 10e-6左右，因为0表示降落。

Good side: you avoid resonance effects. 好的一面：避免共振效应。 Bad side: potentially border-effects, as well as the absence of external source of waves. 不利的一面：潜在的边界效应，以及缺乏外部波源。

This approach is better-suited for qualitative uses: checking the validity of your implementation, looking for model artefacts (eg a maëlstrom-like pattern?) or simply presenting a system that looks organic for an observer. 这种方法更适合用于定性用途：检查实现的有效性，查找模型伪像（例如，类似maëlstrom的模式？）或只是为观察者提供一个看起来有机的系统。