Archive for the ‘fractal’ Category
T-Square Fractal Cubes
If you don’t already know, I like fractals a lot.
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.
Update 3/26/12:
I decided to 3d print it. Printed on a 3d powder printer at Makers Factory in Santa Cruz.
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:
I sent away to Shapeways to get it printed in black plastic.
Fun with an HP 7475 Plotter
So I got an HP 7475 Plotter used. I’ve been playing with it using a Python library called Chiplotle.
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!
In order to get this to work, I wrote a turtle graphics class for the Chiplotle library. If anyone finds this useful, you can grab the code here.
Oh, and here’s a Sierpinski triangle:
Buddhabrot 4-Dimensional Rotation
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.