Chris Huff wrote:

>
> It's too yellow for swiss cheese...
> Hmm, I wonder what a semitransparent Menger sponge would look
> like...it'd probably take a couple years to render with a decent
> recursion level, though. And to get the transparency right, you would
> need to use a completely transparent texture and attenuation (fade_color
> would be useful).
>

Consider rendering a compact subset of R^3 (that is closed and bounded) which
has zero volume but infinite surface area. Thus, it will require infinitely
many recursion levels to trace one single ray accurately through it. And it
would definetely not be transparent, or even semitransparent.

Thus, better and better approximations would tend to a more and more opaque
object which take longer and longer to render. I'd say; skip the
transparency. :)

BTW, the cutaway seems to produce the sierpinsky triangle in the intersection
surface. This might actually be the case!

The menger sponge is actually a generalization of the sierpinsky triangle,
and the s.t. is actually a generalization of the Cantor set. Intuitively, I
think I can see the Cantor set as an intersection between the sponge and some
straight line through it.

Enough rambling, but it _is_ interesting.

~simenkv ( smartass/exessive wiseacre with newly aquired math skills )

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