This is a blog post version of my talk at Bathcamp 2010. I’ve added a few extra links and pointers for some extra background. As a warning this post is heavy on images and video.

The term Fractal was coined by this man:

Benoît Mandelbrot (1924 – 2010)

He’s most famous for a simple equation:

where z and c are complex numbers

But we are much more used to seeing the equation like this

A definition of a Fractal:

A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole

The fractal geometry of nature

Examples exist in natural, such as Romanesco broccoli:

One of the strange properties of Fractals is their dimension

Lines are one-dimensional,

Boxes are two-dimensional,

While a Fractal (In this case a Koch Curve) is one and a bit

So some other famous fractals:

This use the same equation as Mandelbrot Sets but instead of varying c for a fixed z, keeps c constant and varies z.

These follow a grammar, so are great at generating plants and trees.

Mandelbrot sets can also be extended into 3D to create a Mandelbulb

Also Julia Sets can be similarly extend into 4D space producing Quaternion Julia Sets, which can be raytraced on a modern GPU.

Menger sponge is another type of space-filling curve like the Koch Curve above.

This video is of the 128 byte demo called Spongy by TBC, which has also been ported to a 512 byte JavaScript version.

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