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Ruliobiology


Ruliobiology is a proposed framework for studying the generation of biological-like forms by simple computational rules subject to adaptive evolution (Wolfram 2026). It applies ruliology to abstract computational systems rather than to a specific biological organism. A pattern generated by such a system is called a rulioorganism.

The framework builds on a model of adaptive evolution introduced by Wolfram (2024). In the examples studied by Wolfram (2026), symmetric five-color cellular automata evolve from a single non-background cell. The rule plays the role of a genotype, and the resulting pattern plays the role of a phenotype. Adaptive evolution changes the outputs specified by the rule through random mutations. A mutation is retained when it increases or preserves the value of a chosen fitness function, and rejected otherwise. One fitness function is the number of steps before the pattern dies out, with patterns that never die out assigned zero fitness.

Wolfram (2026) uses the term "polyplexy" for the appearance of qualitatively different structures at different scales, in contrast to self-similarity. His examples include repeated modular structures embedded in more irregular patterns. He proposes that the interplay of adaptive evolution and computational irreducibility provides a basis for understanding such forms and their diversity.


See also

Cellular Automaton, Computational Irreducibility, Ruliology

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References

Wolfram, S. "Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes." Stephen Wolfram Writings. May 3, 2024. https://writings.stephenwolfram.com/2024/05/why-does-biological-evolution-work-a-minimal-model-for-biological-evolution-and-other-adaptive-processes/.Wolfram, S. "'Endless Forms Most Beautiful and Most Wonderful': Ruliobiology and the Theoretical Foundations of Biological Form." Stephen Wolfram Writings. Oct. 23, 2026. https://writings.stephenwolfram.com/2026/10/endless-forms-most-beautiful-and-most-wonderful-ruliobiology-and-the-theoretical-foundations-of-biological-form/.

Cite this as:

Weisstein, Eric W. "Ruliobiology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Ruliobiology.html

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