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Author Topic: Sierpinski-Reuleaux, "Spherpinski", and Sierpinski ball  (Read 851 times)
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Nicolas Douillet
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« on: October 06, 2017, 05:49:16 AM »

Hey smiley

Here comes the (first ?) fractal 3D Sierpinski-Reuleaux based tetrahedron. From this, I plan to create some variations later (since my code allow me to "inflate" / "deflate" the tetrahedra)

I am quite proud of it because it is way more difficult to code than the simple Sierpinski tetrahedron, even if in the end the general looking is very similar, for this example at least (and the more you iterate, the closer they look alike). Indeed every Reuleaux is meshed.

I let you check the thing at 4th iteration / level. It is also viewable in my Sculpteo gallery / online 3D printing shop.


« Last Edit: October 18, 2017, 01:09:31 PM by Nicolas Douillet » Logged
Nicolas Douillet
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« Reply #1 on: October 09, 2017, 10:23:10 PM »

Here is the "quadratic 4 deflated" version at iteration 4. The only tetrahedra summits stay unchanged compared to the other versions (Regular Sierpinski and Reuleaux-Sierpinski above)

« Last Edit: October 09, 2017, 10:30:33 PM by Nico » Logged
Nicolas Douillet
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« Reply #2 on: October 10, 2017, 07:32:53 PM »

I created four news variations based on this topic. And some more is to come... wink







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Nicolas Douillet
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« Reply #3 on: October 14, 2017, 10:03:55 PM »

Waclaw Sierpinski and I are glad to introduce you the Sierpinski sphere, which I also nicknamed the 'spherpinski'. smiley It is based on the regular octahedron. I simply performed a meshed Sierpinski triangle on half of its triangular facets, and then projected the result on the unit sphere (simply by norming the vectors). I actually created two versions of it : a simple version with four eighth of the sphere which are empty, and what I call a "double version" - mainly for aesthetical reasons- in which I add a Sierpinski at the centre of each of these four eighth (I don't know if my explanation is clear ?) Here below you can see respectively the simple version at iteration 7 and the double version at iteration 6. Next step is of course the Sierpinski ball, following the same scheme.





« Last Edit: October 15, 2017, 11:03:54 AM by Nico » Logged
Nicolas Douillet
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« Reply #4 on: October 18, 2017, 12:44:02 PM »

So, I am proud to introduce you today the Sierpinski ball smiley

Like all my previous fractal models, it is actually all meshed, as you can see.

Construction principle is roughly the same as the one I used for the Spherpinski (based on the octahedron), except that I needed to find a trick to inflate not only the surface vertices, but also all the interior ones, in the way that it is all Sierpinski ball in Sierpinski ball in... in a word : fractal smiley For this, I used a transformation to compute the multiplying coefficients matrix to go from the octahedron to the sphere (function of latitude and longitude angles).

The surface of the ball is of course equivalent to the simple version of the Spherpinski  above. At first step, four -alternated- eighths of the octahedron based sphere are void. In the end I am very happy with this result since this corresponds to what I imagined before. smiley

I add here three extra views, which are not yet in my gallery. I may also build a 3D printable version, -for me to get a world unique key-ring  grin- and a video / gif



Top / bottom / soltice / equinoxe view




(pi/4, 0) view
 



(pi/4, pi/4) view


« Last Edit: October 23, 2017, 11:40:20 PM by Nicolas Douillet » Logged
Nicolas Douillet
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« Reply #5 on: October 23, 2017, 10:57:41 PM »

The following is now also HERE, especially a nice random convex / concave mix Sierpinski Reuleaux tetrahedron. Feel free to have a look at my gallery of meshed fractals. smiley
« Last Edit: October 23, 2017, 11:26:19 PM by Nicolas Douillet » Logged
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