Biorobotics Laboratory BioRob

PantaRhei
A Simulation Framework for Biological Pattern Formation

abstract

Dynamical systems have become an increasingly interesting tool to engineer biologically inspired control systems. The proper ties that are especially interesting to study, are the pattern generating capabilities of dynamical systems. There are two continuous space models, that have been studied extensively for their ability to generate static and dynamic pattern. Namely reaction diffusion systems and the neural field model. Both classes have been used so far, for different tasks in robotics such as perceptive tasks as well as embodied cognition and motor control. Both systems can be described in the unifying language of dynamical systems, and can be understood as models of activity pattern in continuous neural tissue. To our knowledge no attempt has been made so far to combine those impor tant classes to a generalized class of dynamical systems for pattern formation. In this master thesis such a general class is introduced. Furthermore PantaRhei has been developed for the simulation and visualization of dynamical systems that are governed by this general class of integro-reaction-diffusion equations. It provides a simple scripting language to generate, run and plot dynamical systems of the class of integro-reaction-diffusion systems.

Source:

You can download source of PantaRhei here.

Document:

The document can be downloaded here.

Demos

Schloegl

A Schloegl system is a very simple one species model of a reaction diffusion systems. It is defined by the following par tial differential equation:

The PantaRhei-Script that was used for simulation can be downloaded here.
Movies:
A map plot.
As surface plot.

One Layer Neural Field

The model of the one layered neural field is given through the following equation:

The PantaRhei-Script that was used for simulation can be downloaded here.
Movies:
A map plot.
As surface plot.

There is another PantaRhei-Script for a simular simulation but this time adding diffusion
Movies:
A single layer with diffusion
A single layer with higher diffusion

Two Layer Neural Field

The model of the two layered neural field is given through the following equations:

The activator is:

The inhibitor is:


The PantaRhei-Script that was used for simulation can be downloaded here.
Movies:
A neural field performing a single wave front.
A neural field generating stable spiral traveling waves.

Belousov Zhabotinskii Reaction

The model of the BZ-Reaction is given through the following equations:

The activator is:

The inhibitor is:


The PantaRhei-Script that was used for simulation can be downloaded here.
Movies:
A map plot of the activator (long)
A map plot of the inhibitor.
A landscape plot of the inhibitor.
A slow motion movie of the self-organizing part before a stable traveling waves is generated.
A video in which you can see the inhibititor and the activator side by side.