Computational Morphogenesis

Fri, 03 Jul 2026 00:00:00 +0000

Overview

Alan Turing’s 1952 paper The Chemical Basis of Morphogenesis proposed that the patterns on animal coats, seashells, and fish scales emerge from two chemicals diffusing at different rates. John Pearson’s 1993 Science paper ran the Gray-Scott realization of that model on a supercomputer and discovered a zoo of patterns no one had predicted — self-replicating spots, growing labyrinths, chaotic coral.

This project re-creates and extends that exploration on modern hardware. A 48×48 sweep of the (F, k) feed-kill parameter space — 2,304 simulations, each 8,000 time-steps on a 128×128 toroidal grid, parallelized across 4 CPU cores for 101.8 minutes of compute. Quantitative metrics (Shannon entropy, coverage, standard deviation, dominant wavelength) extracted from every final state. Linear stability theory computed analytically and compared against the simulation results.

Math on Herman

Computational Morphogenesis

Overview