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 discrepancies are large. The balance between these forces produces a sharp phase transition: below a critical decay rate, Blue persists and chromatic diversity is maintained. Above it, Blue collapses and the entire population converges to the Yellow vertex (1,1,0) — maximum capability on two axes, zero on the third.
The post grounds the dynamics from the differentiation operator D(v) on {0,1}³ (Posts 1-2), demonstrates the emergent phase transition through bifurcation analysis, estimates the critical exponent, and visualizes the population trajectory through the binary cube as it falls from random initialization toward a specific vertex attractor. The terminal state histogram shows Red and Green distributed broadly across moderate-to-high values while Blue is compressed into a narrow spike near zero — the chromatic signature of a system that has lost its inhibitory axis.

Five questions for the community:

1. Inevitability of collapse. In any three-axis system where one axis is subject to preferential degradation while the other two are not, is convergence to the two-axis vertex inevitable above some critical decay rate? Or can system topology — lattice geometry, boundary conditions, coupling structure — prevent the collapse entirely?

2. Universality class. The critical exponent β characterizes the universality class of the phase transition. Is the transition in the same universality class as known lattice models (Ising, percolation), or does the three-axis chromatic structure produce a novel class?

3. Negative feedback existence. The feedback loop (Blue decay reduces diversity → reduced diversity weakens error signals → weaker signals accelerate Blue decay) is self-reinforcing above the critical threshold. Is there a corresponding negative feedback loop below the threshold that actively stabilizes Blue, or does the subcritical regime simply lack positive feedback without possessing negative feedback?

4. Yellow maximization. The terminal attractor is the Yellow vertex (1,1,0), not an arbitrary point on the B=0 face. The surviving components are driven to their maximum values. Is this a general property of inhibitory decay in coupled systems — that the loss of the inhibitory axis maximizes the uninhibited axes — or is it specific to the coupling structure defined here?

5. Initial condition dependence. The system was initialized with uniform random RGB values. Does the critical threshold δc depend on initial conditions? Specifically, if the population starts near the Blue vertex (0,0,1), does δc increase, suggesting that initial proximity to the inhibitory axis provides transient protection against its decay?

Notebook included.

https://www.wolframcloud.com/obj/b1180013-2f9d-4af8-a808-8462ddceeb8d

Attachments:

Inhibitory Decay.nb