# Turing Systems

* "A system which has spherical symmetry, and whose state is changing because of chemical reactions
and diffusion, will remain spherically symmetrical for ever... It certainly cannot result in an organism
such as a horse, which is not spherically symmetrical."*

**- Alan Turing**

### Welcome

**Figure:**
*
For example, the spots of a cheetah can be imitated by using a Turing model.
The pattern on the right hand side has been generated by a computer simulation starting
from a random state.
*

These pages are about Turing systems, which are mathematical models describing time-dependent chemical reactions and diffusion. Turing systems possess the characteristic that they evolve towards robust periodic structures from random initial state, that is, Turing systems generate order from disorder. This behavior is of special interest since Turing systems have been shown to imitate many patterns and structures found in nature. Thus, it is plausible that Turing systems could explain some of the chemical mechanisms behind biological growth or morphogenesis.

I studied Turing systems between 2000 and 2004 during my postgraduate studies under the supervision of Dr. Mikko Karttunen, Professor Rafael A. Barrio and Academy Professor Kimmo Kaski. The title of my dissertation was "Computational Studies of Pattern Formation in Turing Systems" (see publications page).

The content is divided to the following pages: