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Published: 2015-10-30 15:40:07 +0000 UTC; Views: 266; Favourites: 2; Downloads: 1
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Description
Menger Schwarz (implicit surface)The first look at the Menger Sponge (level 3) , completely made out of Schwarz minimal surfaces.
When we cut the Menger Schwarz through the plan x+y+z=0, we get some cool hexagrams patterns, as seen in the third image.
The mesh is made out of 37.5 millions triangles with MathMod
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Comments: 10
dark-beam [2015-10-30 15:48:31 +0000 UTC]
Cool idea. consider to try Mandelbulb3d one day?
Edit you are Taha from the forums. I immensely admire your 3d models. Respect !
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MathMod In reply to dark-beam [2015-10-30 15:55:46 +0000 UTC]
Thank you very much dark-beam
I'm not as skilled as you with fractal art but I'm trying to explore the fine line between pure fractal art and conventional mathematical modeling
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dark-beam In reply to MathMod [2015-10-30 16:03:10 +0000 UTC]
not so skilled I am a formula author...
The surfaces in iso form (not the parametric ones) are possible to be included into Mandelbulb3d software... too bad I am busy those days but I will look with great attention!
Count that mb3d does not use meshes so the renders are perfectly smooth. (Like with infinite triangles!)
You will be of course credited.
Cheers!
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MathMod In reply to dark-beam [2015-10-30 16:13:04 +0000 UTC]
I'll try a Menger Schwarz level 4 and publish the iso formulas after some improvements Β
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dark-beam In reply to MathMod [2015-10-30 16:20:50 +0000 UTC]
Cool btw this work looks like an overkill because you obtain a super long formula instead of using a simpler recursion
No offense of course...
Luca
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MathMod In reply to dark-beam [2015-10-30 17:05:30 +0000 UTC]
yes you're right, a simpler recursion is much more easy to work with however I need to eliminate the recursion and work only with mathematical functions in order to calculate partial derivatives, surfaces normales....
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dark-beam In reply to MathMod [2015-10-30 17:46:28 +0000 UTC]
Of course. There are scripts that do so in a few lines of code I can tell you where to find them if you are interested.
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MathMod In reply to dark-beam [2015-10-30 20:25:54 +0000 UTC]
Yes, I'm interested even though I play rarely with fractal-like mathematical functions. Thanks
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dark-beam In reply to MathMod [2015-10-30 22:50:09 +0000 UTC]
the thread is very long but has a huge number of concepts and ideas in it... the genius of knighty!
So take some time to read and understand it.
www.fractalforums.com/ifs-iterβ¦
Menger has two versions plus the sierp pyramids! ...
Happy to help you. See you very soon. Luca
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