Art and mathematics have a long but somewhat strained history. Well, that’s not quite true. It isn’t the intersection of art and mathematics that’s problematic, but our limited ability to understand and appreciate that relationship.
So images that are the result of mathematical calculations are immediately suspect as “not art”, and I’ll be the first to admit that Photoshop filters and Painter brushes that promise to make “paintings” out of photographs make this a very grey area (colorful, but grey).
But the proof, as they say, is in the putting, and the deciding factor is your response to the images.
Fractals are part of a branch of mathematics that embraces infinity, dealing with infinite recursions, infinite depth and capable of generating images represent edges of infinite length, wrapped within themselves in exquisite crinolations.
The term fractal, and the equations associated with it, are the work of mathematician Benoit Mandelbrot, who I wrote about back in June. Others have built on that work and there are a number of variations on the original equations.
One is the algorithm that creates Flame fractals, created by Scott Draves in 1992, graciously made open source and incorporated into Apophysis freeware fractal designing program for Windows, the Corel KPT Collection of commercial filters for Painter and Photoshop and The GIMP open source image editor for Linux and multiple other platforms. There is a central site devoted to Flame Fractals at flam3.com.
So this is a form of mathematically generated images that you, or anyone else, can access and work with. If you view enough images created from this algorithm you’ll begin to see what is inherent in the math and what is the result of the artfulness and vision with which the parameters are manipulated to make images that stand out and are memorable, in somewhat the same manner as photography crossing the line from snapshots into art.
A nice place to start is this gallery of Flame Fractal images created by Roger Johnston on the Tech Republic site. Most of the images are linked to larger versions if you click on them, where you will begin to see the intricate detail of these wispy fantasias.
Images created using this math look as if they are delicately woven from gossamer threads of light, at times astonishingly organic in appearance, suggesting crystaline lettuce leaves, angelic wings or threads of cosmic wool. They are usually isolated into something that might be considered a virtual object or light sculpture composed of delicate lines of color interleaved with sheets of translucent patterns, cascading in not-quite-repetition and leading your eye into whorls of detail.
This kind of computer art invites your imagination to indulge in seeing images within the patterns and textures as readily as Max Ernst’s delerious decoupage, Jackson Pollock’s intricate drip-loop panoramas and, perhaps the best analogy of all, the dreamy “lay on your back on a Summer hillside” fantasies seen in passing clouds.