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"But is it art?"

This is a question I'm often asked by people who understand how fractals are created: if the images arise purely from a mathematical construct, in this case by iterating a simple complex-valued function, how can they be considered art? Doesn't that mean that the images always existed and that humans only discovered them, rather than created them?

My response is usually that the human contribution is in the rendering of an image; therein lies the art. From a purely sensory aspect, we create color maps to render the images visible, sound maps to give the images sound and music; perhaps someday someone will create tactile fractals, fractals which when touched will convey the sensation of the complexity of the image, similarly for odor and taste. 

But the one thing all fractals will have in common, assuming the image is truly fractal in nature, is that they will exhibit self-similarity and the wildly chaotic but deterministic behavior near the boundary of the Mandelbrot set, while within the Mandelbrot set itself everything stops: color is black, sound is silence, etc.

The images

Here is a collection of the images I created  between 1998 and the present, using different techniques. All are inspired by the images I found in the book The Beauty of Fractals, by H.-O. Peitgn and P.H. Richter (Springer-Verlag, 1986), including the image generation parameters. The color maps are my own.