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Author Topic: Paper Fractal  (Read 8061 times)
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combatking0
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« on: October 29, 2008, 02:59:14 PM »

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.


* Cube.jpg (114.99 KB, 1600x1200 - viewed 822 times.)

* cubes3.gif (15.93 KB, 379x460 - viewed 1365 times.)
« Last Edit: October 30, 2008, 01:17:59 PM by combatking0 » Logged
cKleinhuis
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« Reply #1 on: October 29, 2008, 09:49:24 PM »

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

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

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,
« Last Edit: October 29, 2008, 09:51:08 PM by Trifox » Logged

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divide and conquer - iterate and rule - chaos is No random!
combatking0
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« Reply #2 on: October 30, 2008, 10:05:10 AM »

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 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?


* 1-1.jpg (39.45 KB, 1036x999 - viewed 1168 times.)

* 2-1.jpg (77.07 KB, 1159x1102 - viewed 952 times.)
« Last Edit: October 30, 2008, 01:12:14 PM by combatking0 » Logged
cKleinhuis
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« Reply #3 on: October 30, 2008, 01:31:13 PM »

 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 .. cheesy
« Last Edit: October 30, 2008, 01:33:10 PM by Trifox » Logged

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divide and conquer - iterate and rule - chaos is No random!
combatking0
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« Reply #4 on: October 30, 2008, 04:25:38 PM »

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. afro

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.


* 02-11-08_2123.jpg (81.51 KB, 1200x961 - viewed 958 times.)
« Last Edit: November 02, 2008, 11:55:03 PM by combatking0, Reason: Added new picture » Logged
combatking0
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« Reply #5 on: November 09, 2008, 08:55:40 PM »

50% now. Just another 2 or 3 weeks left  cheesy


* 4-1.jpg (79.17 KB, 1200x1164 - viewed 947 times.)
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combatking0
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« Reply #6 on: November 14, 2008, 10:32:46 PM »

62.5% and counting...


* 5-1.jpg (86.54 KB, 1143x1147 - viewed 917 times.)
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combatking0
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« Reply #7 on: November 22, 2008, 10:06:30 PM »

Now at 75% shocked


* 6-1.jpg (78.82 KB, 1125x1139 - viewed 731 times.)
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cKleinhuis
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« Reply #8 on: November 23, 2008, 02:43:05 AM »

nice cheesy
keep on  afro
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divide and conquer - iterate and rule - chaos is No random!
combatking0
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« Reply #9 on: November 28, 2008, 09:49:22 AM »

87.5% complete grin


* 7-1.jpg (74.28 KB, 1110x1173 - viewed 887 times.)
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cKleinhuis
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« Reply #10 on: November 28, 2008, 12:17:16 PM »

you must have a lot of spare time cheesy
this really seems to take up a full week of work cheesy  afro
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divide and conquer - iterate and rule - chaos is No random!
combatking0
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« Reply #11 on: November 30, 2008, 09:52:01 PM »

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.


* 8-1.jpg (81.96 KB, 1111x1175 - viewed 848 times.)
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cKleinhuis
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« Reply #12 on: December 01, 2008, 05:18:46 PM »

 smooth.... the wave

nice work, and the generator is really a little tricky cheesy

well done !
 afro
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divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
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« Reply #13 on: December 01, 2008, 05:21:29 PM »

wouldnt that be a nice toy for kids ? if those paper things were manufactured as pre designed items ?
like lego, fractal lego cheesy
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divide and conquer - iterate and rule - chaos is No random!
combatking0
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« Reply #14 on: December 02, 2008, 03:53:07 PM »

Great idea!

Meccano, Quadro or Magnetix may also be used.
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