The connection between mathematics and art has always been of interest to me, perhaps because I see a lot of potential in this mix that has only been explored on a surface-level with movements such as Optical Art
The department of mathematics at the National University of Singapore has an interesting page from a course called, Mathematics in Art and Architecture
Michael Bach has this collection of optical illusions & visual phenomena.
In discussions of the intersection of mathematics and art, fractal art will inevitably come up. A fractal in mathematics is defined as a geometric shape with a Hausdorff dimension (1) greater than its Lebesgue covering dimension (2).
|“A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same “type” of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.
source:(Mathworld – Fractal)
Examples of visual representations of fractals are plentiful, see for example, Jack Cooper’s Fractal Recursions gallery
[Edited from Photomedia Forum post by T.Neugebauer from 2005-2006 ]