The images on this site are computerized images of fractal equations.
Classical geometry assumes regularity. In fractal geometry we find the formulas that describe what looks like chaos — imagine, for example, the movement of clouds.
Fractals display self-similarity — the pattern of the whole is repeated in the parts.
A good everyday example of a fractal is a head of broccoli. If you look at it closely, you’lll see that the tiniest florets look a lot like the medium-sized florets; and the medium sized florets look a lot like the whole head of broccoli.
Fractal geometry is everywhere in nature. Other examples where you can see this self-similarity are the branching of trees, frost crystals, the surface of the moon, spider webs, the structure of the heart — and it is there in the electrical activity of your brain.
This short video beautifully demonstrates the relationship between nature and numbers.
For examples of fractals in nature:
Fractals in Nature
This is a fascinating website:
The 3D Mandelbulb
If you are interested in reading more about fractals and non-linear dynamic systems, here is an excellent book written for non-scientists:
Chaos: Making a New Science