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Found the link on Wikipedia, so you probably have seen it already (maybe someone here did the animation?)

Anyway I thougt the animation was really impressive:

http://www.pure-mirage.com/html/MillersMengerSpongeFastPlay.htm

O.o impressive what can be done with a stationary camera. GREAT feel for the size :D

I almost got sick by feeling like an atom at the end..  O0

I was very impressed at the beginning and got bored after 5 or 6 iterations when it starts to get really huge, but anyway it is one of the best Menger sponge animation I've seen.

I have to agree with Jeremie, starts off rather well, but soon becomes boring.

Would have been better if there was other objects near by to use as a "size reference".  For example, have the cube be a tiny object between a pair of feet (with shoes on).  Then as it gets bigger, pan out to show more of the person, then with a person and a house, then with a large building near by, and finally a small city.  (Of course it would also need to show those other objects getting crushed in the process.)    :evil1:

But that would really make it great animation!!!   :dink:
 

Now that's an idea for the next Hollywood movie : "The Attack of the Giant Fractal" :):)

A movie came out back in 1957 about this giant block of metal that went around destroying everything in its path.  The "legs" came down from the four corners of the block.  This MengerSponge animation reminded me of that old movie, entitled "Kronos":

   http://www.imdb.com/title/tt0050610/ (http://www.imdb.com/title/tt0050610/)
 

Would you really be crushed by a mengersponge?
Does it have any mass?...  O0

Personally, I say if it has enough substance to be visible, then it has mass.

But which of the three properties of matter were you referring to, when you said "mass":

• inertial mass
• active gravitational mass
• passive gravitational mass

Or did you mean the everyday usage, where mass is often taken to mean weight??
 

I meant, will it kill you if it gets on top of you in earths gravity?

Theoretically it is pierced with an infinite amount of holes, therefore no weight?

(I know the difference between mass and weight, but I guess I meant it has none of it, but I am probably far out as always  O0 )

J

If it has an infinite amount of holes, wouldn't it also have an infinite surface surrounding those holes and therefore infinite weight?

Where's Xeno when you need him??

Back to the way the animation is constructed, it is done by adding small cubes to each other, so it definitely has a mass, but it's not a true fractal. If it were constructed by digging holes in a large cube instead of staking small cubes together, then I would say it has no mass and an infinite surface. And I'm sure anyway it would crush everything down to the nano level and beyond!

if it fell on you, it would cut through you, no matter how much mass it had. Just imagine, how sharp the surface would be.

However, this animations works the other way round.
It grows and grows, so the volume does go to infinity. - It just goes more and more distant so it never hits you. But the base cube always stays the very same size.
This one would indeed have an infinite mass and surface, therefore, the surface wouldn't be as sharp as needed to cut through you without mass.
But as it has mass, it would pretty much squeeze you into an odd shape.

Yuck xD

:D

OK I give up!!!  Under the pressure of nothing...O0

So, if it was a REAL "subtracted" Mengersponge (unlike the animation), you think i would be cut into infinitely small cubes?

COOL way 2 go...

well, it still depends on the Mengersponge's relative size. If there is one of the big holes right above you and you're small enough to fit through, you're save. But don't dare try to climb out of the cube. Your own weight will be enough to let the cube's surface cut through your hand.

All that assumes no Quantum mechanics.
With Quantum mechanics, some incertainity-effects and stability problems will keep the iteration level low enough to avoid any true danger, I guess... In that case, the cube will have mass but it will be extremely lightweight :)

First of all, let's agree on one thing:

Stacking cubes together in that pattern (with successive scaling) produces the same shape as digging it out. Try this: dig out one iteration, then multiply in size by three. It's the same as stacking. Or, if you prefer, stack one iteration of cubes on each other, and divide in size by three. They're all equivalent. In fact, it can even be described by an L-System of a line. So it's equally valid to argue it has no surface area. It's 3D cantor dust, really.

Mass=Density*Volume. Volume=0, so Mass=0. Of course, there's the issue where the gaps become smaller than a planck scale, at which point this all becomes meaningless. On the other, at much higher scales, the gaps become small enough to exclude any air molecules - or at least the soot and dust, which is heavier. So the sponge, filled with these small vacuums, might end up floating up until it reaches clean air. Or it could sink, due to the particles (which [maybe, see next sentence] are still there!). It all depends on whether on not it has mass at a quantum level or not.

Define your terms before you start arguing about them. It's like the monk asking, "How does one attain happiness?", and his teacher responds, "What one earth is that?"

But...  I choose to define the terms differently!

This is a "3D" Representation of an abstract concept  (the image itself is still 2D).

While abstract concepts have no mass, should this object manifest itself in our reality, in such a way that the need to discuss survival should it fall on you ever arose...  it would no longer have the properties mentioned.

Would Cantor Dust have mass?  I say yes!  Folks used to believe Light was massless, but later decided that it does indeed have it.

Also, Cantor dust would not be able to maintain such a rigid structure in the real world if it were massless - so I still think it would be a Massive Object and crush the Frac (tal) out of any humans in it's path  :devil:

You guys! Can't a body dream? Does everything have to be correct in somebodies eyes? It is enough to ask the question and come up with a godzillion of answers! That is the fun! That is my reality :-*

I thought the use of the Devil Smiley indicated that I was only having Fun with the concept.

Besides, such banter and sardonic questioning was the Hallmark of He Who Inspired my user-name, so I feel justified in the statements  O0

I trust all involved in this realize that it's an un-answerable question and the replies here nothing more than Intellectual Gymnastics.  Great fun so long as nobody sprains their brain in the process!

Jeah, I like this too, and was going to put out the fire with gasoline...  :fiery:

If I get hit by an infinite amount of infinitely sharp edges that are infinitely packed together (are they?) how will that affect me?
 :hurt: :hurt: :hurt:

But still posting questions and statements to this topic after the fact anyway!!!   :dink:    :D


Ever seen what ground meat looks like when it comes out of those small holes at the end of the grinder ??   :evil1:
 

That's close, Nahee.
The only two differences: The "cords" of meat all have different sizes and are square :)

Btw, the whole cube would cut equally easy throught the earth, splitting some atoms on its way to the core, lol. (Well, at least assuming, it had any mass.)
If it had no mass, it would basically stay in place where it is and wouldn't ever move from there, but everything that touches it, would be cut into pieces. (Well, additionally assuming, it can't either be affected by any of the other forces^^)