Fractals
Sheep #206 from the early Electric Sheep project, 1993
A beautiful and impressive cross of science and art that bloomed right before my eyes is fractal art. Fractals are purely mathematical objects, characterized by recursive self-similarity and by typically non-integer Hausdorff–Besicovitch dimensions. They’ve been brought into mainstream attention by Benoît Mandelbrot in the 1970s and since then they they’ve been spotted everywhere in nature, from coastlines and clouds to tree leaves and blood vessels. They’ve affected the development of mathematics, adding a great deal of insight on chaos theory, they’ve found useful applications in many fields of physics and chemistry, and they’ve been used extensively to create art, both visual and aural.
Mathematically, fractals can be defined with just a few words, for example the ubiquitious Mandelbrot set is simply the set of complex numbers c for which the orbit of 0 does not escape under iteration of x2 + c (or, simpler, the set of all c for which the sequence 0 –> c –> c2 + c –> (c2 + c)2 + c –> … does not run into infinity). It so happens that fractal images look fascinating to the human eye, in part because so many things that the human eye enounters in nature are of fractal nature: clouds, landscapes, trees, flames, anything where the whole repeats itself in its parts.
An interesting development in the world of fractal art is the Electric Sheep project (www.electricsheep.org) where, since 1999, randomly generated fractal flames are distributed to the human users all over the internet who rate them on their aesthetic appeal, thus providing selection rules for the genetic algorithm which generates new fractals. The image on this page is one of the earliest of those “electric sheep”. Check out their website to see the rather impressive videos of what it has evolved to.