Theoretical Analysis of Morphogenesis
Source: Laboratory of Sick Ideas
Reference: Alan Turing, 1952
This document details the mathematical framework governing the "Reaction-Diffusion" simulation. It explains how organic complexity arises from simple chemical chaos.
The simulation grid represents a "petri dish" containing two distinct chemical substances.
The patterns (corals, loops, mitosis) result from a war between four specific forces occurring in every pixel, 60 times per second.
Chemicals spread from high concentration to low. Crucially, Chemical A spreads faster than Chemical B. This speed difference allows B to form local clusters while A refills the background.
Two particles of B meet one particle of A, and convert it into a new particle of B. It is autocatalytic (self-replicating).
Feed (f): We pump A into the system to prevent starvation.
Kill (k): We remove B from the system to simulate death/decay.
The partial differential equation governing the "Virus" (B) over time:
Translation:
The change in Virus B is equal to:
1. Diffusion (Movement from neighbors)
2. PLUS Reaction (Creation of new B by eating A)
3. MINUS Kill Rate (Death of B)
Why does this create stripes and spots?
When B grows, it creates a "dip" in the local food supply (A). Because A moves fast, it rushes in to fill the void. Because B moves slow, it stays clustered.
This is called Local Activation, Long-Range Inhibition. B encourages its own growth locally, but suppresses its own growth at a distance by depleting resources. The "dead zones" between resources become the stripes of a zebra or the spots of a leopard.
The system is highly sensitive. We exist on a map defined by coordinates (f, k).