Spatial Pattern Formation Models

This repo contains the codes to simulate some spatial models, these are based in the following papers:

1. A. J. Koch and H. Meinhardt Biological pattern formation: from basic mechanisms to complex structures

2. Turing A. The Chemical Basis of Morphogenesis

3. B. Peña and C. Pérez-García Stability of Turing patterns in the Brusselator model

Parameters

The laplace operatur used was:

and the time derivative was approximated as

Activator-Inhibitor

Parameters:

alpha	D	rho	mu	sigma	kappa
a	0.005	0.01	0.01	0.0	0.0
h	0.200	0.02	0.02	-	-

kappa_a was varied from 0.0 to 0.25

Activator-Substrate

Parameters:

alpha	D	rho	mu	sigma	kappa
a	0.005	0.01	0.01	0.0	0.0
s	0.200	0.02	-	0.02	-

kappa_a was varied from 0.0 to 0.07 in steps of size 0.1

Results

Activator-Inhibitor Video

(Click on the image to be directed to the video)

Activator-Substrate Video

(Click on the image to be directed to the video)