Update – This post was written before the release of Silverlight 3.0b, which provides a number of enhancements relevant to this implementation, such as a WriteableBitmap and Pixel Shaders

Rendering

The first obstacle to implementing the RD simulation is that Silverlight 2.0 does not by default provide a means of generating dynamic images. WPF has a WriteableBitmap, but no equivalent exists in Silverlight. However, it does support PNG streams so we can dynamically update a bitmap by encoding it to PNG on the fly. For this I have used Joe Stegman’s PNGEncoder class, which I have modified slightly to deal with RGB data and to reduce memory usage.
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One of Alan Turing’s many contributions to mathematics and science during the 20th century was his 1952 paper on “The Chemical Basis of Morphogenesis” in which he suggested that a simple model of coupled differential equations could account for pattern formation in natural processes such as those found on animal coats. Such models are known as Reaction-Diffusion models, and take the following general form

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The Unlimited Register Machine (URM), designed by Nigel Cutland, is an abstraction of a computer similar to the Turing Machine – but somewhat easier to get to grips with and more in tune with the operation of a modern computer processor.

It also happens to be the model used by the Open University’s course on Mathematical Logic and Number Theory, and is the reason for this article since I studied the course in 2007.

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