Occurrence of non-Platonic self-organization in advanced numerical methods

Determine whether non-Platonic self-organization—where glider-like self-organizing patterns persist only under specific coarse discretization regimes and dissolve at finer, nominally more accurate simulation settings—occurs when using more sophisticated numerical methods for simulating complex systems, in contrast to the forward Euler method studied here.

Background

The paper investigates glider stability across several complex systems (continuous and neural cellular automata, reaction–diffusion, and an Adam-optimizer-based automaton) under varying discretization parameters. It identifies many cases where persistent mobile patterns (gliders) are non-Platonic—i.e., they rely on specific discretization artifacts and lose stability when simulation resolution is refined—contradicting the usual expectation that finer discretization improves fidelity.

While the study focuses on systems implemented with the forward Euler method, the author raises the broader question of whether similar non-Platonic self-organization would persist when simulations employ more sophisticated numerical methods commonly trusted for prediction (e.g., higher-order or implicit schemes). Establishing this would clarify whether the phenomenon is tied to Euler-like update artifacts or is a general property of complex-system simulations.