Archive for the ‘fractal’ Category
A few months ago I was playing around with the T-Square fractal. Recently I decided to revisit this fractal and try to add another dimension. So instead of using squares, I decided that I’d use cubes and make the rules the same. For each free corner on a cube, create another cube and repeat.
So I wrote a small program in Python that creates a scene for Povray (speaking of which, I wasn’t able to find any good libraries for talking to Povray in Python! If anyone knows of such a library, I’d love to know.)
Anyway, here are the results:
I’d love to make a video out of this but I don’t think my budget can afford it right now. The frame you see above you took about an hour or so to render on my laptop. Unless anyone has a cluster they’re willing to lend me, I’ll have to stick to stills for now.
In order to get it made into a proper 3d file, I actually ended up writing a Python script for Blender, you can find that here. Turns out that scripting Blender is way easier than writing .STL files — just to write a cube you need to define a bunch of vertices’s and get them all in the right order or the normals are screwed up.
Update (again) 4/16/12:
Recently I’ve been making fractals on it. Here’s a Hilbert curve I made:
Hilbert curves are space filling fractal curves. This means that when iterated to infinity, at no point is there a straight line; thus it is a curve. Very neat!
Oh, and here’s a Sierpinski triangle:
I’ve been playing with fractals recently. More specifically, the Buddhabrot fractal.
The Buddhabrot set is closely related to the Mandelbrot set:
The mandelbrot set is displayed on the complex plane, where one axis is the real component of (we’ll call it ) and the other is the imaginary component of (a.k.a ).
With the Buddhabrot set, we can add a few more axes. Instead of just using and , we also use the real and imaginary components of as axes. Whereas in the Mandelbrot set, is assumed to be , in our 4D Buddhabrot set, we make these values variable as well.
So instead of the two dimensional image you’re used to seeing of the Mandelbrot set, we’ve instead got 4 axes: and .
Which leads us to our next problem — how do you visualise a 4 dimensional object on a computer? Well, it’s difficult. You obviously can’t just draw an image of it, or even just show a 3 dimensional picture of it. Instead, we show it rotation in 4 dimensional space.
So, here’s the result:
I’ve made all of this code open source — here’s the project page.