Last week I showed some of the possible patterns that were available as solutions of mathematical equations. This week we end morphogenesis month by showing you how to create such Turing patterns for yourself.

Freely available at:

Freely available at:

is a simulator (written in java) of the types of reaction-diffusion patterns that we have been considering. The supplementary information section gives a really nice overview of how Turing patterns work and how to use the software. However, for those amongst you who are too impatient to read such things click on the picture below to show a brief manual of how to use the program.

The main joy of this program is that you are able to alter the parameter values of the reaction diffusion equations, seen in the big box at the bottom, very quickly. Thus, you are able to experience different patterns being created right in front of your very eyes! Below are a few that I created in 5 minutes that easily show you the great complexity available through this simple mechanism.

Each simulation starts with a smiling face initial condition like the one seen below.

The first pattern occurs when the program is run with the default initial conditions. Clearly, we see that we get multiple line patterns framing the happy face. Altering the parameters slightly produces spots and stripes as seen in the second picture, giving the face a much more surprised look. Pushing the parameter values even further we generate oscillating patterns as shown in the two snapshots on the right, thus, the face changes colour rapidly. Finally, for certain patterns it is difficult to make out the initial condition at all. In the bottom image the solution oscillates but in waves across the domain.

Hopefully, you'll have some fun exploring the many different patterns you can get. Whilst you are generating complex structures think about how difficult it must have been for Alan Turing to have postulated these patterns without our moden day computers. He never saw the patterns that now bare his name, yet, he managed to construct the framework by which we understand them.

Finally, if these have entertained you and you would like to see even more peculiar patterns then try Tim Hutton's youtube channel. Through combing different types of models he was able to produce oscillating Turing patterns (seen below). Now they are really trippy!

Hopefully, you have enjoyed morphogenesis month as much as I have had making these posts. I deal with Turing's theory of morphogenesis everyday and it is such a beautiful subject that I decided everyone must know about it.

Next week, back to the normal mathematical silliness.

Each simulation starts with a smiling face initial condition like the one seen below.

Initial condition |

Click on the picture to make the images clearer. |

Hopefully, you'll have some fun exploring the many different patterns you can get. Whilst you are generating complex structures think about how difficult it must have been for Alan Turing to have postulated these patterns without our moden day computers. He never saw the patterns that now bare his name, yet, he managed to construct the framework by which we understand them.

Finally, if these have entertained you and you would like to see even more peculiar patterns then try Tim Hutton's youtube channel. Through combing different types of models he was able to produce oscillating Turing patterns (seen below). Now they are really trippy!

Hopefully, you have enjoyed morphogenesis month as much as I have had making these posts. I deal with Turing's theory of morphogenesis everyday and it is such a beautiful subject that I decided everyone must know about it.

Next week, back to the normal mathematical silliness.

**________________________________________________________________**

**________________________________________**

**References:**
Java software: http://www.sciencemag.org/content/329/5999/1616/suppl/DC1

Oscillating Turing pattern: http://www.youtube.com/watch?v=QCbdYGD1m3Y&list=PL35FD96A5F8236109

Oscillating Turing pattern: http://www.youtube.com/watch?v=QCbdYGD1m3Y&list=PL35FD96A5F8236109