Below are a couple more scenes I made with the same software. Every one of these scenes is created the same way: by defining a simple master object (a basic line drawing like a triangle or other polygon), and then cloning it a few times, scaling and positioning each clone to define how the fractal iterations will develop. The results are rendered in real time, which is what makes the program so easy to play with.

As you can see, these fractals strongly mimic natural patterns we are all familiar with, suggesting that fractal structures are building blocks in the physical world. I spent maybe 10-15 minutes on each of these; more time or expertise with the software could yield more realistic results.

Personally I am very intrigued by art based on math. To the uninitiated, mathematical art may sound very plain, rigid, boring. However, it is possible to mathematically construct very beautiful and intricate designs. Fractal theory suggests that many objects in the natural world, appearing complex or even chaotic as a whole, are actually built from relatively simple mathematical repetitions (examples would be tree branches, sea shell patterns, snowflakes).

Music is also a prime example of art with a mathematical basis: timing, rhythm, and harmonics are all based on math. (The degree to which two given notes harmonize is related to the alignment/correlation of the “peaks” in their respective sine waves.) It is often alleged that many of the great classical works have strong patterns that can be mathematically derived, and this is perhaps true on a lesser scale for other genres of music.