Category: Nonlinear Dyn.

Summary: Testing whether modest short-range spatial correlations in Game of Life initial states create a window with more gliders and longer-lived activity than uncorrelated or strongly clustered soups.

Random starting states in Conway's Game of Life can produce rich moving structures, but the effect of controlled spatial correlation is much less mapped than the effect of overall density. This experiment asks whether short-range correlations create a middle regime that favors gliders and sustained activity, while stronger clustering instead suppresses mobile structures by over-aggregating the initial pattern.

The simulation sweeps across fixed live-cell densities and several correlation strengths, then follows the automaton long enough to sample late-time behavior. By comparing correlated soups against IID soups at the same density, the script isolates whether mesoscale structure in the initial condition changes the balance between mobile debris, persistent activity, and over-clustered collapse.

That framing turns a familiar cellular automaton into a geometry question about initial disorder. The experiment is aimed at identifying a genuine correlation window, not just cataloging another set of random soups.

Method: Repeated Conway's Game of Life simulations sweeping initial live-cell density and short-range spatial-correlation strength, with late-time occupancy sampling.

What is measured: Late-time glider occupancy, sustained activity, dependence on initial density and correlation strength, and evidence for an intermediate optimum.