Newton Biomorphs: Mind Toys

A biomorph is a mathematical object that reminds the viewer of a living organism. Richard Dawkins, an implacable advocate for the theory of evolution, showed that evolving biomorphs wasn’t difficult as part of his effort to show evolution is a pretty normal, standard process in our universe. A youtube video of a lineage of biomorphs is available here.

The shot above is an example of biomorphs that I borrowed from a web page about code for creating your own biomorphs. Biomorphs are a staple example in computational biology, though they are way off at the theoretical end. I work as a computational biologists and, mostly, I perform analysis of DNA and other molecules. Today’s Occupy Math is a chance for me to show off a type of biomorph I invented. We’ve already done a blog about fractals, and today I want to look a fractal biomorphs.

The picture is a Newton’s method fractal. It is created by specifying a function and then checking which parts of the plane are mapped, by Newton’s method, to which place the function is zero. Each color corresponds to a different place where the function is zero. Use the “view image” function in your browser to look at the full-sized picture. You can see many of the connected chunks of the picture look like microbes or small crustaceans. Its not hard to pick them out and make fractal biomorphs.

Of course I played with the colors and things a little with my photo-shop like software, but this is another example of a kind of art you can do with mathematics. I use these images as monsters in my role-playing games. They can be used as checkers or chess pieces too. Which one is the king? Occupy Math hopes you have enjoyed our demonstration of the kind of things you can do once you get used to math.

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics


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