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How do typical glaberish and Lenia CA compare?

One apparent difference is that most Lenia rules from Chan’s taxonomy ¹ (Interactive online zoo here) form Turing patterns from random uniform initializations.

Examples of continuous CA: a) CA evolved with random fitness b) Lenia CA from Chan’s taxonomy ¹ c) CA in glaberish evolved for roughly even chances of random initial grids vanishing d) CA in glaberish evolved by selection for vanishing unpredictability ²

What about capturing the differences between CA dynamics with an information-theoretic measure ³

1. Convert grid to 8-bit integer format

2. For each neighborhood-sized window in the grid:

   • Compute relative proporitions of each of 256 cell values
   • Compute entropy for each cell location according to

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1. Chan, Bert Wang-Chak. “Lenia - Biology of Artificial Life.” Complex Syst. 28 (2019): https://arxiv.org/abs/1812.05433. ↩ ↩²

2. Davis, Q. Tyrell, and Josh Bongard. “Selecting Continuous Life-Like Cellular Automata for Halting Unpredictability: Evolving for Abiogenesis.” GECCO Companion Proceedings (2022). https://arxiv.org/abs/2205.10463 ↩

3. Entropy and other information theoretic measures abound for making sense of CA complexity. See the background and references in the paper for more examples. ↩

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