3D IFS fractal: Menger Sponge Zoom

[Lulzisback33]

My brain hurts i think ill go lay down for a while...

[Hulsie]

FAKE. THIS ISN'T A REAL SPONGE AT ALL.

[Selur91]

You could make a gif!

[LaszloBencze]

This is nice but it would be better if the zoom were much slower so the self similarity could be better appreciated.

[CaptainChaos]

Nice. Tip for next time though: don't compress the video so much. The compression artefacts make it next to impossible to see exactly what's going on...

[MakinMagicFractals]

@CaptainChaos

It wasn't - YouTube screwed it completely when they changed the fornat :(

[FluffyBunniesOnFire]

It's a 2.7268-dimensional subset of 3-D space.

[WrexsouI]

This gesucks.

[blessedchild501]

what is the original object supposed to be , explain more please why fractals are called fractals. ahhh i dont know anything

[MakinMagicFractals]

The Menger Sponge is a 3D IFS fractal - IFS = Iterated Function System.

For more details on the Menger Sponge see the relevant article on Wikipedia.

For brief details on fractals also just look at the relevant document on Wikipedia.

If you want to know more about fractals generally then just Google for "fractal yale" without the quotes and go to the link for Fractal Geometry.

[AllFractUp]

Has anyone successully used IFS Builder to run a 640 x 480 animation of the Sierpinski's Cube? That was the object you were looking at. I ran the program on a P4m 2.2 GHz machine for 28 hours and only had 100 frames of aniamtion to show for it. But when I had to kill the program I lost all the work I had made.

[MakinMagicFractals]

@AllFractUp If you have Firefox 4 and a video card that is/was anything like top-of-the-range less than 2 years ago then try browsing to "fractal.io".

[therewasnoIDfree]

@MakinMagicFractals Thank you VERY much for showing me this uber cool website! - Everybody who has a good computer HAS to go to "fractal.io" and make cool images! It's so much fun!

[dkamm65]

It'd be insane if someone made this for real.

[boatofcoins]

fractals are all around you man. You're just a set of interlocking fractals. your thoughts are fractal in nature. everything is infinite. I know i sounded high there and i am, but what I'm saying is true. Our minds affect our reality. The way you perceive something is entirely up to you, but it is very hard to have your own concrete thoughts and your own perspective when bullshit media is flying at your face telling you how to act, talk, THINK; subliminally. Wake up to the NWO, peace in 2012.

[aevasic]

im high

:o

[fireball1127]

...?

[alexvegas]

If you add '&fmt=1' to the URL it plays correctly. It's the HQ version which is messed up.

[MakinMagicFractals]

Hey - thanks for that !

[sharpezor]

wat

[ZylonBane]

This would *probably* be a really cool video, if the excessive compression hadn't rendered it illegible.

[MakinMagicFractals]

It wasn't anywhere near as bad originally as it is now, YouTube have obviously changed something !!

[elseandortheother]

NO not the BLOCKHEADS!!!

[Psalm23YHVH]

explain for me someone what Mandelbrot fractal is and what is the point of this? where in real life can zooming in like this be applied?

[disorder269]

Draw a sphere around it and you enclose a specific volume. The thing is that the cube covers infinite area so you have an infinite area inside a very well known volume. Something like the universe maybe.

It is not a mandelbrot and i am not sure if it should be called a fractal. No fraction geometry involved here.

[Supuhstar]

Check any reliable source. It's a different fractal than mandelbrot, called a "fractal curve"

Menger sponge is a fractal curve. It is the universal curve, (it has topological dimension one, and any other curve [more precisely: any compact metric space of topological dimension 1] is homeomorphic to some subset of it).

In layman's terms, it'a a fractal that, no matter WHERE you zoom in on it, it resembles the whole PERFECTLY.

[Starhawk73]

Trippy!

[slipcurve]

fractals rule

[swomplode]

Fake

[MakinMagicFractals]

Well, computer generated but not "fake" - try it for yourself in Ultra Fractal (the formula is mmf4.ufm:3D IFS).

[GandaraVideos]

I like the design and the infinite fractals. Amazing with what you can do with fractals these days.

[mirabilis]

that thing has no volume! :D and infinite area. :P

[mirabilis]

I've changed my mind, I don't know if the area is infinite. Somebody? :(

[Supuhstar]

surface area is infinite, volume is zero.

[VCat2006]

If this thing has a surface, then it must also have a volume. Am i missing something?

[Supuhstar]

The surface, as well as the volume, is theoretical.

[MakinMagicFractals]

An infinitely thin surface has no volume.

[VCat2006]

True, but this thing doesn't appear to have a surface either.

[MakinMagicFractals]

If you follow the construction of the Menger Sponge from the 1st stage hole removal onwards you'll see that at each stage the volume decreases but the surface area increases.

So in the (theoretical) infinite limt the volume of the Menger Sponge is zero but the surface area is infinite.

[VCat2006]

A surface with infinite holes?

[Alfaris]

I *think* an infinite (3D) fractal has a zero volume and zero area. Because if you think about it the area gets smaller and smaller the more you split the figure up, so eventually one specific area will be 1/infinity = 0, then you add all those 0's together to get 0. Same thing with volume. Also the perimeter of each 2 dimensional part of the fractal increases to infinity.

That's just what I think please don't hate me if I am wrong because I am pretty new to these things called fractals.

[acridplacidity3]

the volume is zero, but I am pretty sure the surface area is infinite. Its just like the cantor set.

[Alfaris]

Yea that makes sense, because everytime it is split you give it more surface area (I was thinking of 2D fractals). The surface area plays the same role as the perimeter in 2D fractals, since it surrounds the volume the same way the perimeter surrounds the area. Also, you never split the area in the first place, only add to it.

[mirabilis]

The volume shrinks 20:27, and the area grows 20:9 by every itteration, if I have calculated right. :) (20/27)^infinity = 0 and (20/9)^infinity = infinity. (You take the original figure, shrinks it to a third of the original size. Make 20 of this new shrinked figure and build a new figure).

[mirabilis]

...sorry! By a third of the original size i mean a cube thats 1x1x1 becomes (1/3)x(1/3)x(1/3) = 1/27 of the original size/volume.

[MakinMagicFractals]

0 volume, infinite surface area is correct.

[8mad0manc8]

So that shape has zero volume and infinite surface area what shape has Infinite volume and Zero Surface area and thus no shape i wonder ?

[CrazyMixx]

"what shape has Infinite volume and Zero Surface area and thus no shape i wonder ?"

. Could be the Universe...

[hypnospirit]

Spongebob under the microscope! Yay!

[hl2alyx]

this is exactly the image i got stuck in after i smoked salvia, eternal loops are scary.

[jesusxfreak]

It's funny, because the cube itself doesn't exist.

[MakinMagicFractals]

Only in the same way that an infinitely thin plane doesn't exist :)

As proof that it doesn't exist consider rendering the infinite limit of the opposite of the cube i.e. start with what are the 7 "holes" in the original Menger cube as the solid part and the 20 solid parts as holes then replaces each of the 20 holes with a reduced size copy of the whole and repeat at every scale thereafter - the infinite limit result is a complete cube even though the Menger sponge is "missing".

[Rensra]

holy shit that shit's hilarious when you're high!

[Broadsmile1987]

It is really great, You can zoom every part of the fractal as much as You want, and You will still get the patterned boxes. A masterpiece :)

[Broadsmile1987]

Wow, this sponge is the best fractal I ever saw. So deep and with good quality...

[jamierourketen]

one of the most interesting things i have seen on you tube! thanks for your imput.

[jamierourketen]

did i write imput! lol! drinking way to much wine!

[jamierourketen]

i live in that apt block...

[MakinMagicFractals]

How many levels deep ? :D

[SnakeDragonFish]

I want one!

Well not actually, 'cuz that thing really creeps me out..

[somedude07]

MIND FUKKKKKKKKKKKK

[somedude07]

MIND FUCKKKKKKKKK!

[ElSickOz]

nice

[gemstonehelix]

AAAAAAAAAAAAAAAAAA!!!!!!!!!!!!­!!

[tomshoot]

Amazingly hypnosis concept !

Peace

[Elphaba555]

woah, what was the cube made of, more importantly how did u zoom in so well???

[MakinMagicFractals]

It's a 3D IFS fractal rendered using the escape-time method rather than the usual contractive methods.

The problem with zooming using the usual contractive methods is that you basically have to calculate the entire object even if you only want to see a bit of it whereas the escape-time method ray-traces, testing each ray to see if it collides with the fractal and if so then finding the nearest collision point i.e. only on-screen pixels are involved.

[zombierobopirate]

lolwut

[psikoladrama]

UAAAAAAAAAUUUUUUUU

[sultanek]

O_O