Talk:Menger sponge

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This math block:

M_{n+1} := \left\{(x,y,z)\in\mathbb{R}: \exists i,j,k\in\{0,1,2\}: ((3x-i,3y-j,3z-k)\in M_n)\mbox{ and at most one of }i,j,k\mbox{ is equal to 1}\right\}

is too wide to fit on mid to small size screens (1024px or smaller). Could someone familiar with the notation find a good way to break it into two or more lines?

I'd suggest breaking it at the colon (before the 3x-i part) though I can't figure out how to get that to work. That's the point where it switches from describing the set it's a part of to giving the formula (basically). 68.47.64.155

Contents

[edit] Incorrect?

[[Image:Gasket14.png|thumb|3D [[Sierpinski carpet]]]]

3D Cantor dust
3D Cantor dust

I was editing the page Cantor dust, (adding a image of the 3D version of the set). There I found, the text talks about a 3D version of the Cantor dust and names it "the Menger sponge". But this page shows a 3D Sierpinski carpet. The images to the right shows the difference. Does anybody what's correct? // Solkoll 22:59, 29 Dec 2004 (UTC)

Both are correct, just different generalizations of the Cantor set in three dimensions. Both the Cantor dust and Menger sponge have the Cantor set within them, but also space around the Cantor set that is not directly described by the set. This space around the set is described by extending the set into multidimensions, but there are multiple ways to interpret the pattern of the Cantor set, as it does not directly define its construction in more dimensions. Pengwy 02:33, 22 May 2006 (UTC)

[edit] Sponge?=

It might be good to explain why this is a "sponge" and not a cube or something else.

[edit] Universality

I mentioned this at Lebesgue covering dimension too, "any object of Lebesgue covering dimension one" doesn't embed in the Menger sponge if "object" means "topological space". I think the right version needs "compact" and "metrizable". I'm going to put a "disputed" note but the article is misleadingA Geek Tragedy 15:06, 11 February 2007 (UTC)

[edit] Guisi aka SILK

In case anyone cares, there is a 2006 Taiwanese film called Silk that uses the Menger Sponge as a plot device. The scientist in the film uses the menger Sponge construction to try and come up with an Anti-Gracity device but winds up instead capturing a form of energy we would call a ghost. There's a fair amount of visual representation of the sponge. Neat film but it's a horror film with science fiction overtones. It's IMDB entry is here:

GUISI - Lisapollison 07:22, 27 February 2007 (UTC)

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