Monday, August 20, 2007

Serial molecules

One of the well-known properties of the Mandelbrot set is that it's full of smaller, distorted copies of itself. I've just found out that Mandelbrot himself refers to these as "molecules," which I think is a wonderful name for them.

Over the last week or so, I've been doing a lot of systematic exploring of the Mandelbrot, trying to get a better feel for the patterns around the molecules, and how those patterns are affected when you zoom into different sub-regions of them. It's fascinating; they distort in all sorts of ways, and I'm getting better at predicting and working with the distortion to find the shapes I want.

I must confess, though, that so far the results have been embarrassingly silly. This week I plan to post a series of single-layer Mandelbrot zooms, the reaction to which will probably be the same hollow groan that follows a really bad pun. To begin with, the image that started me on this exploring binge in the first place.

Pink Hearts

The magnification is 2.3422469x1020. I've surrounded them with thorns, because it seemed suitably poetic, or symbolic, or something.

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