Mathematical Beauty

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry." - Bertrand Russell

1/28/10 - http://en.wikipedia.org/wiki/Mathematical_beauty

The above image is an example of "Fractal Art." Fractals are based on a geometric principal of self-similarity. What this means is that essentially the final product (or the whole) is based on infinitely smaller and repeated patterns. Here is a less complex example of a fractal:

As you can see, what starts as a simple pattern soon becomes relatively more complex and detailed simply by repeating it's pattern upon itself. This concept can be applied in great complexity and detail as to create fractal art such as these:

Mathematical Beauty can be defined in other ways as well. Some believe that the interconnection of theorums and infalliable truths of mathematics is beautiful. Much like an intricate puzzle, all of the pieces fit together so perfectly as to form a (yet unfinished) masterpiece of symbolic logic and an underground network of natural mechanics.

Please read about one of the following from http://en.wikipedia.org/wiki/Mathematical_beauty and comment:

1. Beauty in Method

2. Beauty in Results

3. Beauty in Experience

4. Beauty in Philosophy