Fractals as Art

Paint by numbers, or something more?

Science and art have a complicated relationship. Can a photograph be art in the same sense that a painting can be art? If you think "No," look at Ansel Adams' Winter Storm picture from his Yosimite Valley protfolio, and consider the question again.
To some extent, fractal geometry - or more precisely, the easy computer generation of intricate fractal images - heightens the tension of this debate. Yet we are not so convinced there is a problem. Many uninformed programmers have produced fractal "art" that is just plain ugly. An early instance of this involved modifying the standard Mandelbrot set algorithm to start each iteration with some point other than the critical point z = 0. The resulting images often looked like Mandelbrot sets that had been run over by heavy trucks; we call these images Mandelbrot roadkill. In fact, producing interesting images requires not only an aesthetic sense, but also some understanding of the mathematics. This may be compared with the fact that a painter must have some understanding of the mechanical properties of paint flow.
To illustrate the way in which fractals blur the boundary between science and art, The Beauty of Fractals is an elaboration of a series of art exhibitions, displayed internationally under the auspices of the Goethe Institute.
More recently, the March/April 2000 issue of the Ylem newsletter is on "Fractals as Art. See
Here are some examples of fractal art from a 1999 contest. More information can be found at Click each picture for an enlargement.
All these images are generated by programs with specific parameters for the formulas to be iterated, the assignment of colors, and so on. To be sure, a subtle hand is required to reliably produce interesting images. Yet the very parameter dependence opens a new avenue: evolutionary art. Steven Rooke and Julien Sprott have approached this issue in different ways.
Another posibility is to combine the approaches of Sprott and Rooke: in Rooke's genetic algorithm assign fitness by something like Sprott's numerical invariants instead of Rooke's visual inspection. Of course, aesthetic sense probably cannot be quantified by only a few numbers, and perhaps it is appropriate to leave in the thumbprint of the artist.
A good example of seeing the artist's ideas in a fractal is this picture by Kerry Mitchell. Click to enlarge.
Mandlebrot Meets Mondrian