Greg Klein's Blog

T-Square Fractal Cubes

with one comment

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:

T-Cube Fractal

T-Cube fractal iterated 9 deep

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.

And a 3d print of the fractal with only 6 iterations this time.

Update (again) 4/16/12:

I sent away to Shapeways to get it printed in black plastic.

3d printed fractal from Shapeways

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Written by gregklein

February 17, 2012 at 5:03 pm

Posted in fractal, math, python

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  1. Hi, I found your page through image search on t square fractal. I think these 3d prints are very interesting (I had wanted to do this exact thing in my imagination). Interesting because of surface area. If you think about it, these objects have as much surface area as you could possibly fit in the space they take up (I think anyway). It seems like there must be a practical purpose for an object like that don’t you think?Like if it was meant to absorb something out of a liquid or something, just a thought.

    Brady

    April 6, 2013 at 9:07 am


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