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| A continuous-state cellular automaton on [0,1]³ where each cell carries an RGB vector. One axis — Blue — is subject to preferential decay through habituation, while a competing error-detection mechanism restores Blue when local chromatic... |
| A chromatic cellular automaton on {0,1}³ generates a cruciform pattern from a single seed (established in Post 3). At every timestep, the null-space complement of the pattern — obtained by mapping each state s → 7−s — is computed and compared to the... |
| A single Idea seed placed at the center of a 4-dimensional stochastic cellular automaton — two temporal layers coupled to a spatial grid — evolves through five semantic states: Idea, Concept, System, Flaw, and Dead. The update rule has three... |
| Every positive integer contains a perfect countdown. Reduce the products of N's multiplication table modulo N+1 and the residues descend: N, N-1, ..., 1, 0. The proof is one line — N ≡ -1 (mod N+1) — but the structure it reveals when placed inside an... |
| The unit cube {0,1}^3 — the RGB color lattice — contains a geometrically distinguished axis: the principal diagonal from (0,0,0) to (1,1,1), along which all coordinates are equal. This diagonal is the null space of the differentiation operator... |