Diff — Cellular automaton

Revision #2406 → #3068 · back to history

modifiedContinuous endomorphisms of shift spacesbd3590895f34

Field	From #2406	To #3068
mathlib.decl	—	Subshift
mathlib.match_kind	—	generalization
mathlib.module	—	Mathlib.Dynamics.SymbolicDynamics.Basic
note	Shift spaces and their continuous endomorphisms are not formalized in Mathlib as such.	Mathlib defines `Subshift` (closed shift-invariant subsets of the full shift), but not the Curtis–Hedlund–Lyndon characterization of CA as continuous shift-equivariant endomorphisms.
status	not_formalized	partial

addedVon Neumann's 29-state self-replicator7bd42d030030

addedExistence of self-replicating pattern (200,000 cells)3f827883de11

addedWolfram classification (formal statement)820a413d48ac

addedClass 2 partition into fixed-point and periodicff0df8ecc709

addedRule 110 universality (proven by Cook)65f88e4fb3fa

addedNext-nearest-neighbor CA rule space (2^32)6ef0813fb627

addedBelousov–Zhabotinsky reaction as CA89f4ac4d0563

addedLattice gas automataf7bc9da4fcf5

addedBiological lattice-gas cellular automata125d975d520c