Menger Sponge Rendering

[cwjean76]

My brother has asked me to produce a 3d model of the Menger Sponge for him. It is a theoretical object having an infinite surface area but holds zero volume. I'm know very little when it comes to 3D. I'm trying to learn. I mostly do 2D and isometrics. I have attempted producing this using the old 2 point perspective method.....but it's VERY time consuming. :banghead:

Can anyone give me any ideas on how to go about this? I, basically, just don't know where to start. Should I use a solid or separate surfaces, etc? I would like to be able to render the surface of the object and have shadows.

I have attached an image of this object to give you an idea of what I want it to look like.

Thanks in advance for any and all ideas leading me forward in this little project.

I'm using AutoCAD 2007.

[gblack.127549]

It sounds like your brother is having a joke at your expense. If the object exists only in theory you won't be able to model it.

If on the other hand you want a facsimile like the picture you showed take a small cube, pierce some holes in it using the subtraction tool and stack it up to build the object. Then sew it all together with the union tool.

Can you design me a perpetual motion machine when you are done?

[cwjean76]

It sounds like your brother is having a joke at your expense. If the object exists only in theory you won't be able to model it.

All I know is that the theory was first introduced in 1926 by mathematician Karl Menger while exploring the concept of topological dimension. Theoretically, it never ends, this is just a representation of what it might look like. Modeling it only takes it so far. It goes to infinity as numbers never end.


If on the other hand you want a facsimile like the picture you showed take a small cube, pierce some holes in it using the subtraction tool and stack it up to build the object. Then sew it all together with the union tool.

I'll try starting there. Thanks.


Can you design me a perpetual motion machine when you are done?

I'll get right on that....:lol:

[jaberwok]

You probably don't have to model all the holes.
If you can paint a picture of one face you can apply it as a material - picture + bump map + opacity map.

[cwjean76]

.....pierce some holes in it using the subtraction tool and stack it up to build the object. Then sew it all together with the union tool.

I will say that this is taking up quite a lot of resources and REGEN time is extremely long. At one point, I tried the union tool...once it was about 50% done and AutoCAD tells me to use BREP instead of UNION. How will this affect the outcome. I read that it gets rid of the original history of the primitive solid.

[cwjean76]

Can you design me a perpetual motion machine when you are done?

Not my design...but, here you go!