Fractal architecture

A few days ago, I went to the library and took out the book Fractals: Form, Chance and Dimension by Beniot B. Mandelbrot. I am fascinated by fractals because they appear so often in nature. I don't have any evidence to back it up, but intuitively it makes sense that nature would employ fractals so readily. The algorithms required to generate fractals are recursive and require very few instructions -- which makes them perfect for Minecraft architecture. (I can't think of how to use them in real life problems yet, so I'll have to start with virtual problems)

Temple of the Exponential

I want to design bad-ass structures and geographical features so that when players enter my Minecraft server, they can be inspired to create some of their own. In the past, I've used math equations to produce things. For example, the temple of the exponential:

The problem with this structure is that it was very complex to design and required a lot of work on my part. The exponential didn't naturally manifest itself into a 3D structure that would look cool.

Now, fractals, on the other hand, are very amenable to construction. So far I've made a world-scar gorge of peril which can be used to house an immense city or could contain some interesting paths. Either it will become a national part of a massive industrial complex. It depends on the will of the people. I constructed it using a Quadratic Koch Fractal of dimension 1.5. Check it out:

Fractal world scar

You can think of the pattern like this:

How to build Quadric Koch Fractal

You start with just a line (or in Minecraft, a row of cubes). Then, you divide the line into 4 segments. Next, move block #2 'up' and you move block #3 'down'. Finally, on every 'edge' that touches air you do the same thing over again. It's really simple but it makes beautiful shapes.

When combined with other fractals, you can really make some triumphant structures. The total area never changes because if you have four blocks, you just move one up and one down. Quadric fractals are best for Minecraft, since you can only build with blocks. I will add more as I find them!