[Plugin] Menger Sponge 1.0

[Plugin] Menger Sponge 1.0

Postby Regular Polygon » Fri Aug 06, 2010 3:39 am

This plugin is strictly just for fun. The Menger Sponge is a 3D fractal in the Mathematics world. In the computer graphics world you can only draw the first few levels before it becomes too complex to render. However, it still has an interesting self-similar shape, which makes it possible to build using a plugin.

It is constructed iteratively. You start with a cube. Scale the cube down to one third the size, and make 27 copies arranged like the cells in a Rubik’s Cube. Then remove the cube at the middle of every face, and remove the cube in the center, leaving 20 cubes. Merge them together so there are no coplanar edges. This gives you the first level.

level 1.png


The second iteration is the same process, only instead of a cube, you start with the first level sponge, scale it down, and translate 20 copies as before.

level 2.png


The third level is constructed from 20 copies of the second level sponge, and so on. Below is an image of the fourth level, which is probably about as far as you want to go. It has 200k faces, and takes about a minute to generate all the geometry.

level 4.png


You can color the outside by clicking on the component with the paint bucket. The inside faces have a different color for each level. You are not stuck with my color choices. They are grouped by material. So, just open the component, and apply the paint bucket to any face. That will paint all the faces that are the same color.

There is more documentation, and a link to download this plugin, here: Menger Sponge 1.0.

Thanks.
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Last edited by Regular Polygon on Fri Aug 06, 2010 7:31 pm, edited 3 times in total.

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Re: [Plugin] Menger Sponge 1.0

Postby Rich O Brien » Fri Aug 06, 2010 8:34 am

Thank you for this, useful and interesting, plugin
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Re: [Plugin] Menger Sponge 1.0

Postby Didier Bur » Fri Aug 06, 2010 1:43 pm

Welcome Sierpinski and Menger to SCF !
But I don't agree with Regular Polygon when he says on the plugin's page "It is constructed iteratively". I'd say it is constructed recursively, that's the opposite and the basis of the fractal algorithm. Or did I miss something ?
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Re: [Plugin] Menger Sponge 1.0

Postby Regular Polygon » Fri Aug 06, 2010 6:50 pm

Hi Didier,

You are correct, the implementation is recursive. What I mean by iterative is that the construction is a repetitive process, where each level is built up from subcomponents of the previous level in the same way.

Nice to see someone is checking the source code. :thumb:
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Re: [Plugin] Menger Sponge 1.0

Postby remus » Sat Aug 07, 2010 9:37 pm

Cool plugin. I do enjoy a bit of maths geekery :)
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Re: [Plugin] Menger Sponge 1.0

Postby d12dozr » Mon Aug 09, 2010 7:16 am

Very cool plugin, RP...so many new plugins, so little time... :mrgreen:
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Re: [Plugin] Menger Sponge 1.0

Postby Starling75 » Wed Aug 11, 2010 2:01 pm

Menger in the field
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Re: [Plugin] Menger Sponge 1.0

Postby Regular Polygon » Wed Aug 11, 2010 7:23 pm

Starling75 wrote:Menger in the field


Abstract art at its best. :thumb: :lol:
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