Several features of reaction-diffusion systems make them particularly promising candidates for computing by chemical reaction: They are capable of exhibiting varied and complex, ordered behaviour; different forms of r-d systems can sustain both stationary structures and information transmission over long distances with little loss, by means of excitation waves. Another useful property of certain r-d systems is their ability to cause some reagent to migrate towards areas where that chemical is already concentrated, making it possible for those systems to select for the highest among several peaks of concentration, which is crucial for the modelling of a Kohonen network, among other tasks.
One reason for the interest in chemical computation is simply the possibilities opened up by moving away from the digital computational paradigm in which almost all computer science to date has been conducted. Nobody knows where this might lead, but it is not unreasonable to suspect it might take us somewhere interesting. Another reason is the importance of chemical systems in the information processing performed by real brains and nerve cells.
The propagation of electrical signals within neurons is known to work by reaction-diffusion, and there is some reason to believe that substantial information-processing takes place on this level. In addition to this, the interaction between neurons in the brain and modulatory chemicals which spread by diffusion may be modelled by reaction-diffusion equations. It has become clear only relatively recently that these diffusing neuromodulators play a major role in brain function, and the details of this role are still being worked out. We have so far only seen the beginnings of work exploring the coupling between digital analogues of these chemicals and traditional neural networks.