2D Reaction-Diffusion: Patterns in Chemistry and Biology

What is Reaction-Diffusion?

Reaction-diffusion systems describe how two or more substances interact and diffuse through space. These interactions can lead to the formation of complex spatial patterns due to the interplay between reaction kinetics and diffusion rates.

The Gray-Scott model, specifically, simulates a system where two chemical species A and B react and diffuse in a medium, leading to the emergence of various stable or transient patterns.

How Does It Work?

In the Gray-Scott model, the reaction between substances A and B is governed by the equations: ΔA = f * (1 - A) * B - k * A + DΦ^2A, where ΔA represents the change in concentration of substance A over time, f is the feed rate, k is the kill rate, and DΦ^2A is the Laplacian diffusion term.

The diffusion terms are calculated using a 9-point stencil approximation on a discrete grid, reflecting how substances spread out from high to low concentrations.

Why Does It Matter?

Understanding reaction-diffusion systems helps in modeling various natural phenomena such as the formation of patterns in animal coats, skin pigmentation, and even the growth of bacterial colonies.

These models are also crucial for applications like chemical engineering, where they can predict the behavior of complex mixtures under different conditions.

Real-World Examples

The Gray-Scott model has been used to explain the patterns observed in the skin pigmentation of animals. For instance, it can simulate how stripes and spots form on a tiger or zebra.

In biology, reaction-diffusion systems are also relevant for understanding the development of organs during embryogenesis.

Frequently asked questions

Try it live

Everything above runs in your browser — open 2D Reaction-Diffusion (Gray-Scott) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.