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Strictly speaking, you cannot create a true fractal using origami, and even I'm cheating by using glue to hold it together, but I'm wondering if anybody can tell me what type of sponge I have created in the attached images.

I know it's not a Menger Sponge, and I'm struggling to find a name for it.

The first one used 1152 squares of paper. The second one, in theory, would require 16992 squares of paper.

what the heck did you do ?
fold a whole lot of paper to look like this ? RESPECT!  O0

that one is cool, can you upload an how to ? so i can show it my nephew :D

inf fact you have generated a menger sponge with an irregular generator, e.g. one big whole and many smaller around, i do not know if those types have a special name, great work !

the gallery would be a better place to refind it later on,

A how to guide? I hadn't thought of that.

I'll get some bits together. So far the new one is roughly 25% complete, and I'm taking pictures of it every 12.5%, so there are some pictures on my computer somewhere.

(edit)
I have found a decent Sonobe Diagram (http://www.math.lsu.edu/~verrill/origami/sonobe/ori0.gif) and here are the first 2 pictures of the level 2 Menger Variant (attached).

I'll post an in-depth how to guide soon.

BTW, are fractals allowed to have an overlapping generator, or is that what you might define as irregular?

 :smooth: :smooth:

whao, those loke pretty, how do you get the inspiration for the base form ?

very nice

in fact you are using a method i called alternating fractal, this means you have 2 generators, and alternate them in each step
in this case you used this generator at first iteration in 2d:


and the generator for the first paper fractal, hm, it is the first iteration of a more complex iterator,
perhaps i will post an example program to let you experiment with alternting menger sponges .. :D

The base form came from an idea I had many years ago about gluing multiple dice together to form a cubic shape with lots of holes. Since paper is more readily available than dice, I have changed the construction method somewhat.

The isometric image was drawn in MS Paint using repeated cut and pastes. I have a 5th iteration image, but no browser will render it as it is HUGE. I'll try to zip it and attach it in all its glory.

I suppose that would apply to the coloured sections, but the overall shape is a single 3d fractal.

I'm using multiple colours to keep the price down. There will be 4 colours in all.

I look forward to seeing the program. O0

I have taken some pictures of how to turn a group of 6 sonobe units into a simple cube, and some more pictures detailing how to join 72 sonobes to make a first-iteration Menger Sponge. I'll put a link to the new website I'm creating for it soon.

(edit)I have now completed 37.5% (3/8) of my paper fractaloid. See attached.

50% now. Just another 2 or 3 weeks left  :D

62.5% and counting...

Now at 75% :o

nice :D
keep on  O0

87.5% complete ;D

you must have a lot of spare time :D
this really seems to take up a full week of work :D  O0

I got a bit delayed at the start of last week.

Here's the finished article.

I'll try to start a level 3 version soon.

Further consideration has led me to believe this is a quite a simple variant of the classic Menger Sponge with only 1 generator. The generator is moved 2/3 of a cube in each direction, instead of a whole cube. There's 4 lots of 2/3 in 3, which is why the extra holes appear.

 :smooth: :worm:

nice work, and the generator is really a little tricky :D

well done !
 O0

wouldnt that be a nice toy for kids ? if those paper things were manufactured as pre designed items ?
like lego, fractal lego :D

Great idea!

Meccano, Quadro or Magnetix may also be used.

http://www.youtube.com/watch?v=T3j3UEOPBJ8

i just found another nice paper fractal, a valentine special
http://extremecards.blogspot.com/2009/02/fractal-pop-up-valentine.html
 O0 O0

Although these paper fractals are quite interesting, and very cool to look at when they are completed, I think there are better ways to spend one's time.    ;)     Not to mention, "greener" ways to build fractals.

The above fractal building video is a brilliant find! It puts my current efforts to shame :(

I agree that there are greener methods to building fractals, but nothing beats the ability to see and feel a fractal right in front of you. Just looking at it on screen has a limited appeal to me. Everyone has their own opinion.

Since finishing my stage 2, my wife won't let me build the stage 3 model until I can sell the stage 2. I have all the post-it notes I need to build stage 3.

Does anybody know of a suitable market place for 3D paper fractals?

In order to gain permission from my wife to build the next size up, I have resolved to sell the Level 2 cube on eBay (http://cgi.ebay.co.uk/Cube-of-Mystery-2008_W0QQcmdZViewItemQQ_trkparmsZ72Q3a1683Q7c66Q3a2Q7c65Q3a12Q7c39Q3a1Q7c240Q3a1318QQ_trksidZp3286Q2ec0Q2em14QQhashZitem140308908797QQitemZ140308908797QQptZUKQ5fartQ5fSculptureQ5fGLQQsalenotsupported).

If you know anybody who collects modern art, please let them know about this.

It's not just about the money - its about getting the space to further the development of the Variant 12 Menger Sponge.