I drew another fractal today, the Koch Curve (click on the graphic for full size). The Menger Sponge took more time, and by rights I should be more satisfied with it, but the Koch curve is somehow nicer to me, it's simply elegant.
The curve is formed by starting with a line, and in the centre third, creating an equilateral triangle. This is repeated for every one of the four lines we now have, and so on.
The fractal dimension is around 1.26, this is because to make curve we have had to use four smaller copies, each is a third the linear dimension. I.e. To increase the size 3 times we need four copies.
3dimension=4, so dimension=ln(4)/ln(3).
Like the Menger Sponge I drew the koch curve freehand.
It was just one of several sketches I drew today. Of the 'arty' ones, I'm quite pleased with the water.