Section 3

Table of Contents

Section 5

 

4. Edenīs model

The application of reaction-diffusion models is limited by one key assumption originally made by Turing: the medium on which the reaction-diffusion takes place, be it a surface or a line, does not grow.

One of the first computer models of growing biological structures was proposed by Eden [Ede1960]. Eden's model is very simple. The simulation takes place in a square grid. A single initial particle is placed in the center of this grid. The subsequent particles are attached, one by one, to randomly chosen points on the border of the structure formed in the previous steps.

A sample structure obtained this way is shown in Plate 8. The colors indicate the state of the structure at different points in time. A structure developing according to Eden's model is roughly circular.