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Many simulated complex systems that support persistent self-organizingpatterns, i.e. gliders, have a 'state-plus-update' paradigm. This approach canbe found in computational models of physics, continuous and neural cellularautomata, residual connections in neural networks, and optimization methodslike stochastic gradient descent. If the update is the output of a differentialequation and modulated by a step size parameter, we have the familiar andgeneral Euler method. Generally, a smaller step size is expected to yield moreaccurate results, at the expense of more computations to arrive at a desiredend point.  I examine multiple systems supporting gliders that fit into the Euler methodframework, including multiple approaches to continuous cellular automata andthe Gray-Scott artificial chemistry system. Each of these systems yield one ormore glider pattern-rule pairs that persist under specific, and sometimes quitecoarse, discretization conditions, but become unstable at nominally moreaccurate, finer simulation conditions. These patterns (in combination with thesystems they persist in) are clearly not approximations approaching an abstractideal as discretization tends to zero, but exist on their own, somewhatbaffling, terms that include the systematic errors of particular discretizationregimes.  I refer to these gliders as 'non-Platonic'. Code for replicating or expandingon this work has been made available athttps://github.com/RiveSunder/DiscoGliders.

Discretization-Dependent Dissolution of (Dis)Continuous Gliders: Non-Platonic Self-Organization in Complex Systems