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2013-04-28 Lattes Julia sets
2012-10-21 3d hyperbolic limit sets
2012-07-01 Fractal sea creatures
2012-06-24 Nicholas A. Cope
2012-06-16 3d printed Julia set
2012-05-06 Pep Ventosa
2012-04-06 Fractal automata
2012-03-30 Periodic Julia patterns
2012-03-25 Conformally invariant patt...
2012-03-21 In Flight
June 16th 2012
3d printed Julia set
In this post, I'd like to report on some experiment with 3d printing. The dense fractal patterns I am currently interested in are dense Julia sets of rational maps, and they naturally live on the sphere (check this blog post).
To create a 3d object out of these, one can use the fractal pattern as a heightmap on the sphere (i.e. use it to deform the sphere along the surface normal according to the color). I used Ultra Fractal to generate the heigtmap, Blender to create the 3d object and Shapeways to 3d print it.
The fractal I picked for this first attempt is one of the simplest Lattès Julia set (more about those in a future blog post hopefully), depicted in 20120504-1. Here is the result:
More photos of the printed model are available here. For reference, I used the "Frosted Ultra Detail" material offered by Shapeways. The outcome is not completely satisfactory. I had to make the sculpture very small (5cm x 5cm x 4.5cm) to keep the cost reasonable. I also had to lower the original polygon count (to about 200000), because Shapeways' server would not accept the model. That's why the details are somewhat washed out. For comparison, here is a 3d model rendered with a better polygon count (and maybe a slightly steeper heightmap):
Still, it's a great to see and feel it as a physical object. Below are (textured) 3d models of other dense Lattès Julia sets. More models can be found here. I can't wait for color high-resolution 3d printing to be widely available...
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