LifeFind

A simple and naïve Game of Life pattern searcher written in Wolfram Language.

这是个用来搜索生命游戏（以及别的 Life-like 的元胞自动机）里的图样的 Mathematica 包。搜索方式是把图样要满足的条件看成一个 SAT 问题，然后用 Mathematica 自带的 SatisfiabilityInstances 函数求解。灵感来自 Oscar Cunningham 写的 Logic Life Search。

这个包就是写着玩的，搜索速度慢得离谱，完全无法搜索周期稍大的图样。如果需要实用一点的搜索工具，推荐使用 Logic Life Search（可搜各种图样），或者 ntzfind（专搜飞船）。更多搜索工具见《生命游戏搜索程序汇总》。

我不怎么懂编程，代码肯定有很多 bug。遇到问题欢迎来提 issue。

以下是简短的英文说明。详细的用法见维基（仅中文），或者使用范例。

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This is a Mathematica package for finding patterns in life-like cellular automata. Inspired by Oscar Cunningham's Logic Life Search, it converts the problem to a SAT problem, and solves it with the built-in function SatisfiabilityInstances.

Usage

This is a Mathematica package, so you need Wolfram Mathematica. Here is a installation guide for any Mathemaica packages.

After the installation, you can load the package with

<< Life`

The main function in the package is LifeFind. LifeFind[x, y, p, dx, dy] will try to find a pattern with size (x,y), period p (default = 1), and translating (dx,dy) (default = (0,0)) during a period.

For example, this may find 25P3H1V0.1:

LifeFind[5, 16, 3, 1, 0]

You can specify the rule and the symmetry with options "Rule" and "Symmetry" (see the screenshot above). The default rule is "B3/S23" (Conway's Game of Life). The supported symmetries are the same as Logic Life Search.

If you can read Chinese, please read the Wiki or these usage examples.

Supported rules

• Totalistic and non-totalistic life-like rules
• Totalistic and non-totalistic hexagonal rules (hexagonal symmetries are not supported)
• The corresponding Generations rules.

The output for Generations rules might be incomplete: there might be "dying" cells outside the bounding box. I will not fix this.

If "Rule" is set to "", it will search in an unspecified rule, and return both the rule and the pattern. This is extremely slow, and the rule string is not simplified.