Menger's sponge

This one’s for Rivenwanderer…

It’s a level 4 Menger’s sponge. I was just rumaging about on the internet today and came across some stuff about this.

It was pretty easy to make… only took about 20 mins… and then about 2 hours messing about with lights and textures to make it look prettier :smiley:

Nice! Umm… why me…? Do I know you? I didn’t think I was all that visible in the Blender world any more… is confuzled

Very nice… I always like to see fractal images and this is a very nice representation. If you can be bothered you may want to look into Sierpinski as he came up with the original ‘gasket’ idea behind these particular fractals.

Keep it up

Pretty cool!


/me suddenly feel the urge to do that same in LightFlow and with a crystal raytraced material…



No you don’t know me! I just stumbled across something while furkling around on the internet…

Cast your mind back… to November, in the year 2000…

Gandalf82 Guildsman posted 11-17-2000 06:52 AM
Curious about the title of this thread? You should be. This is a little site I’ve developed and I’ll update it as frequently as I can. Mengermania! It’s a site devoted to something I’ve been working on for the past 10 weeks or so. Well now it’s 11 I think. I’ve lost track! Check it out. Tell me what you think. Am I too obsessed?

calyxa Guildsman posted 11-18-2000 10:57 AM
I started making a Menger sponge in Bryce last night – got to the point where duplicating four sub-groups was taking around three hours or more… decided to wait on finishing the last level of the sponge 'til after I can archive some stuff to CD today…

rivenwanderer Guildsman posted 11-18-2000 01:16 PM
Those are cool! I’ll have to see if I can make one in Blender! Although, without a Boolean kin 1000 d of operation in Blender, it will be closer to doing it by hand than in Bryce…

calyxa Guildsman posted 11-18-2000 01:26 PM
you don’t need booleans at all, just cubes.8 cubes around the bottom (middle one missing). same thing for the top. then, fill in the sides with ‘corners only.’ that becomes your basic unit. group it, then use that group as if it was a plain cube and construct the same sort of object… 8 groups around the bottom, same thing for the top, fill in the sides with groups at the corners only… group this thing again… repeat… 'til your machine bogs down trying to duplicate the groups of cubes…

rivenwanderer Guildsman posted 11-18-2000 02:19 PM
lol… I’ve done that, more or less: make a plane, extrude it until it’s in a 3x3 grid, extrude that until it’s a 3x3x3 cube, and delete/fill in the necessary faces, making heavy use of the SNAP menu so they are all exactly perpendicular to each other, then duplicate them, snap them to the grid, join them as one object (uses less memory) and continue, as calyxa said, until your machine is too slow to move around in (duplicating hasn’t been a problem so far)… I’m on level three and slow, but manageable (I’ve made indoor building scenes that slowed it more than this). I’ll post a picture of it as soon as I get it as big as it will comfortably go.

[Gandalf82 Guildsman posted 11-18-2000 03:36 PM
Wow. I didn’t think I would make people interested in making this thing.
What’s the equation?..ummmmm…duhh…
I have no idea!
Calyxa, there is an easier way to get a level 3 without making your computer crash in Bryce, but making a level 4 makes your computer crash no matter which way you do it!

rivenwanderer Guildsman posted 11-18-2000 03:44 PM
I’ve made a level 4 in Blender . But I can’t make a higher level, because I got it to work by placing each level 3 cube in a separate layer, and I’m out of layers! Now I just need to give it a decent texture(s) and render it. I’ve only had illegal operation errors two or three times. But it is very very slow to move the view around, even with each in a separate level!

rivenwanderer Guildsman posted 11-18-2000 05:49 PM
Well, I sort of got it to work. See here I’ll probably delete the .blend file soon due to the size (see the page to see exactly how big) and the fact that it can be made in one day if I should ever need it.

Gandalf82 Guildsman posted 11-18-2000 05:55 PM
Um…Rivenwanderer? That is a very cool object, don’t get me wrong, but that isn’t a Menger’s Sponge. VERY cool pic though! Name it somehting. Name it the Rivenwanderer Sponge!

rivenwanderer Guildsman posted 11-18-2000 06:28 PM
Hmmm… you’re right. Must have mis-duplicated or something. I’ll rename it soon.
PS- it is true, though, that the pictures make some faces look like they’re on the same plane as some other faces when they really aren’t.

calyxa Guildsman posted 11-21-2000 04:59 PM
here’s that level 3 sponge I made in Bryce. the scene file is only 19MB - I’ve had larger files… but it did run but of memory once when 1000 I tried to change the material on all the cubes a second time. I’d managed to change them from a metal texture to glass… but then when I tried to change’em back to another material, that’s when it died on me… don’t know if I’ll mess with this again or not, though I may have to check out this notecard thing more thoroughly.

stejah’n Guildsman posted 11-21-2000 05:42 PM
I made one in bryce, but I coudln’t get past level 3. It would crash. Man I wish I could.
That is awesome.

Gandalf82 Guildsman posted 11-21-2000 06:59 PM
Using another method other than duplicating many, many cubes, I DID get very close to a Level 4, but after I made things negative and positive, it died, but I got close!

That was the edited highlights, btw, not the whole thread.

I found it on a page entitled “RivenGuild Backup Project” and the link is

The link to the whole thread is

Come on then bogbean…how have you managed to do it (especially in 20 mins) I’m dying to know…pleeeeeease :stuck_out_tongue:

DAMN! you suckup.

did you actually save those posts? an i’m sure it has nothing to do with rivenwanderer being one of few females around here :slight_smile:

Ah, I see! Heehee, I miss Rivenguild… I wish the archive project was easier to search, there’s a lot of history there. I should try to do a menger’s sponge now with doubles removing and important things like that :wink: Oh, and I made a sort of cross between a menger’s sponge and a serpinski {or whatever triangle} a while ago; it’s in 3 desktop sizes on this page :slight_smile:

[edit] Hey… lobs a @ Goofster what does being a girl have to do with fractals?

Okey dokey, here’s how to make it.

I did a quick run through to test my instructions and it only took me 4 minutes to make it this time!

1.) Add cube (in centre) in top view, TAB to get out of edit mode
2.) Scale to 0.5 using Ctrl
3.) Duplicate with Shift-D, hold Ctrl, move 1 unit right
4.) Duplicate with Shift-D, hold Ctrl, move 1 unit right
5.) Select 1st and 3rd cubes
6.) Duplicate with Shift-D, hold Ctrl, move up 1 unit
7.) Select bottom row of cubes (3 of them)
8.) Duplicate with Shift-D, hold Ctrl, move up 2 units
9.) Select 4 corner cubes
10.) Switch to side view
11.) Duplicate with Shift-D, hold Ctrl, move up 1 unit
12.) Select bottom row (8 cubes)
13.) Duplicate with Shift-D, hold Ctrl, move up 2 units
14.) Switch back to top view
15.) Select all 20 cubes
16.) Join with Ctrl-J
17.) TAB to get into edit mode, select all vertices, hit remove doubles button
18.) TAB back out of edit mode

Repeat 3.) through 18.) but moving 3 times the distance
Repeat 3.) through 18.) but moving 9 times the distance
Repeat 3.) through 14.) but moving 27 times the distance

At this point you should have a level 4 sponge.

It looks like there’s a limit in Blender that stops you from joining the meshes at this level, due to the number of vertices in a single mesh (is it 64K per mesh?).

I tried to go to level 5 but my computer ground to a halt as it ran out of memory (only 128MB at the moment) - those of you with more might be able to get a level 5?
The level 4 has 312,320 vertices and takes up 14MB memory. I don’t know what the limit is in Blender for the total vertices in all meshes but the level 5 would need 20 times this (6,246,400 vertices and 280MB). It’s also more difficult to duplicate, as the 20 cubes in the level 4 can’t be joined. You could put them in layers to make it easier.

Anyone got 6GB of memory to try for a level 6?

Hey… go for it - I’d like to see what it looks like in crystal!

I’ve put some instructions in an above post… give it a whirl.

Oh, and I made a sort of cross between a menger’s sponge and a serpinski {or whatever triangle} a while ago; it’s in 3 desktop sizes on this page :slight_smile:

Very nice - I like the lighting.

[edit] Hey… lobs a @ Goofster

Neat emoticon… got any other good ones?

How about… whats your sign? :stuck_out_tongue: j/k with ya

whoa looks comploictaed…looks like something from hellrasier, great stuff

Yeah I was thinking of the box from Hellraiser too… uncanny similarity.

I tried to make a level 5 menger for fun and it tramatized my poor computer. I almost had it…in fact I made the menger itself but I could no longer move the view or shift in order to take a picture. Plus the save file was around 1 gig…the horror. Thats a cool level 4 menger though, before this post I didn’t even know what one was! :slight_smile:

Thanks Bogbean for the lowdown on the technique…I’m definitely giving that a go.
I may try a level 6 just as soon as I can get some network cards for my 3 CRAY5’s that I have humming away in the basement…if only :wink:

How about… whats your sign? :stuck_out_tongue: j/k with ya[/quote]

Blast! Rumbled again! 8)
Now she’s never going to want to have my children. I’ll just have to figure out some other way to get rid of them… sulphuric acid maybe… :wink:

Anyway, we Scorpios aren’t gullible, we don’t believe in all that astronomy nonsense.

Cool, very good modeling, and busy by the sounds of your procedure there!!! :wink:
Do you think you could do a fairly accurate Hellraiser puzzle box if you had a good reference pic or 3, 'cauze THAT I would cool to see!!! :wink:


Blend on, and blend well!!!

Already done. A crystal raytraced Sierpinski gasket was my old avatar. It’s on my site – it took about 3.5 hours to render. I tried going up a level, and it was 18% done at 24 hours, so I stopped it.