Category: Nonlinear Dyn.

Summary: Mapping how the transient growth or decay exponent in Conway’s Game of Life changes with the initial live-cell density.

Conway’s Game of Life is famous for its complex collective behavior, but most studies emphasize a few standard starting densities rather than the full dependence on the initial occupation fraction. This experiment asks how the transient power-law exponent varies as the starting density sweeps from very sparse to nearly full.

The simulation runs large random initial conditions across a high-resolution density grid and fits the resulting time dependence of the live-cell density. It looks for the crossover from low-density growth to high-density decay, and for a critical density where the fitted exponent changes sign.

That turns a classic cellular-automaton observable into a crossover-mapping problem. The payoff is a more complete curve for how microscopic initial density selects between different transient dynamical regimes.

Method: Large-grid Game of Life sweeps over initial density rho_0 with power-law fitting of live-cell density trajectories.

What is measured: Transient density exponent alpha(rho_0), critical sign-change density, asymptotic density, and crossover-curve shape.