CA随机3色 [英] CA Random 3 colors

问题描述

是否存在随机的元胞自动机规则(如规则 30)并且有 3 种颜色?

解决方案

这更像是一个研究问题 - 您必须对您发现的元胞自动机 (CA) 规则进行统计测试，以证明它是随机的.如果您想做这样的研究项目，请查看

如果您有 Mathematica - 很容易发展 CA(并使用 卡方检验来进一步测试它们的随机属性一>).这就是您如何从 NKS 书中的图片设置 3 个颜色范围 1 个总体 CA(您可以使用 假设检验):

ArrayPlot[CellularAutomaton[{#, {3, 1}}, {{1}, 0}, 50], Mesh ->真的，PixelConstrained ->7、颜色规则->{0 ->白色，1 ->红色的}，结语 ->文本[样式[规则"<>ToString@#, 红色, 粗体, 25], {50, 340}]] &/@{177, 912, 2040}//列

Does exist a Cellular Automata Rule that is RANDOM (like the rule 30) and has 3 colors?

解决方案

This is rather a research problem - you have to run statistical tests on the Cellular Automata (CA) Rule you find to show that it is random. If you would like to do a research projects like this check out The Wolfram Science Summer School.

For now let see what information and tools can get you started.

First of all I would read Chapter 6: Starting from Randomness - Section 5: Randomness in Class 3 Systems in the "New Kind of Science" (NKS) book and surounding chapters for better understanding of the subject.

I would also look at many free apps exploring 3-color rules at The Wolfram Demonstrations Project.

Next you can start from good candidates found on page 64. Follow that link and read the image captions about 3-color CAs with seamingly random behavior. The online book is free (you may need to register once). I would recommend also reading pages 62 - 70 exaplaining those images.

Also take a look at "Random Sequence Generation by Cellular Automata" by Stephen Wolfram.

If you do no thave Mathematica, then Wolfram|Alpha can provide tons of valuable information. Here are the queries for the CAs from NKS book: rule 177, rule 912, and rule 2040. Not how Wolfram|Alpha gives you, for example, difference pattern images - higly divergent (spread fast) means chaos and randomness:

If you have Mathematica - it is easy to evolve CAs (and further test their random properties say with Chi-squared test). This is how you set up a 3 color range 1 totalistic CAs from pictures in NKS book (you can dig further with Hypothesis Testing):

ArrayPlot[CellularAutomaton[{#, {3, 1}}, {{1}, 0}, 50], Mesh -> True, 
    PixelConstrained -> 7, ColorRules -> {0 -> White, 1 -> Red}, 
    Epilog -> Text[Style["Rule " <> ToString@#, Red, Bold, 25], {50, 340}]] & /@ 
{177, 912, 2040} // Column

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