Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns

The paper empirically demonstrates the existence of two‑dimensional, area‑spanning sub‑structures (“areas”) in the 3D Young activator–inhibitor CA on a three‑torus and gives a positive answer to the prior conjecture, but does so by extensive simulation and visual classification rather than a rigorous proof. The candidate solution provides an explicit, rigorous construction: a finite 3D torus with parameters (N,R1,R2,ρ) = (10,4,5,ρ), and a slab configuration whose DC/UC interface is planar and which is a fixed point of the CA; because this state occurs with strictly positive probability under the i.i.d. Bernoulli(ρ) initialization, it witnesses existence. We independently verified the sign pattern of the update sums layer‑by‑layer; the configuration is indeed a fixed point. Thus, both are correct, but via different methods: the paper by experiment and the model by explicit construction.