VCML Paper 107: Turing Universality Across ctrl -- Logic Is Generic, beta=1/phi Not Required

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Authors: Gabriel Aubin-Moreau
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Abstract

Tests whether VCML Turing universality is specific to ctrl=0.680 (beta_eff~1/phi) or generic across ctrl. Repeats Paper 106 Parts B and D across ctrl in {0.650, 0.665, 0.680, 0.695, 0.710}. Part D (collision logic): outcome range = 0.163-0.178 at ALL five ctrl values (threshold 0.05). Logic demonstrated at 5/5 ctrl values. The collision outcome pattern (f(w=16)~0.611, f(w=32)~0.568, f(w=48)~0.437, f(w=64)~0.511) is identical across ctrl with no systematic trend. Part B (wall velocity): domain wall experiment is confounded by (a) dead-phase instability (dead fixed point phi*=-15 is alive at all tested ctrl) and (b) periodic-BC wrap-around causing the wall to collapse within 11 steps. Wall velocity measurement is inconclusive. Main conclusion (STRONG): VCML logic gating is generic; the Heaviside gate alone suffices for Boolean computation. beta=1/phi is not required for universality. Open question: does beta=1/phi optimize any computational property (signal fidelity, gate density) even if it does not gate universality? Paper 108 will test perturbation propagation speed across ctrl via localized pulse expansion in equilibrated background.

Fields of Study & Subjects

Cellular Automata and Applications Nonlinear Dynamics and Pattern Formation Advanced Mathematical Theories and Applications

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
13 March 2026
Language
EN
Document type
Preprint