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Author Topic: Some experiments with the Menger sponge  (Read 1363 times)
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Max Sinister
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« on: April 30, 2016, 08:18:33 PM »

After learning a bit about 3D printing and the STL file format, I decided to write a program from scratch to create STL files. First, I used it to make a simple cube, then I added recursion to create a Menger sponge.

After this, I did the math to make a "Menger roof" and a "Menger star slice":


(Pictures are screenshots from STL Viewer.)

More pictures will be coming...


* menger_sponge.png (70.61 KB, 640x650 - viewed 209 times.)

* menger_stars2.png (71.02 KB, 600x580 - viewed 236 times.)

* menger_roof.png (35.97 KB, 650x420 - viewed 197 times.)
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Max Sinister
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« Reply #1 on: May 02, 2016, 03:59:26 PM »

Now I'm trying different proportions.

First, 1-2-1:

Second, 2-1-2:

Next challenge: More irregular proportions.


* menger121.png (63.98 KB, 660x630 - viewed 184 times.)

* menger212.png (21.5 KB, 625x600 - viewed 161 times.)
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Max Sinister
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« Reply #2 on: May 06, 2016, 09:31:36 PM »

OK, this one was broken:



* stars_wrong.png (94.28 KB, 675x650 - viewed 185 times.)
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Max Sinister
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« Reply #3 on: May 06, 2016, 10:45:04 PM »

The "Menger roof" and "Menger star slice", this time dividing the sides 1:2:3 instead of 1:1:1.



* roof123.png (44.17 KB, 400x470 - viewed 376 times.)

* stars123.png (143.56 KB, 600x570 - viewed 196 times.)
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Max Sinister
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« Reply #4 on: May 09, 2016, 11:27:08 PM »

Now I'm adding even more variables: Along the x-axis, the proportions are 1-2-1; along the y-axis, 2-1-2; and along the z-axis, 1-2-3.

Gives a very strange effect - a mixture of order and chaos. Not to say, uncanny.



* strange.png (227.29 KB, 700x666 - viewed 197 times.)
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cKleinhuis
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« Reply #5 on: May 10, 2016, 12:01:29 AM »

i played around with the obvious back then like this:

define a 3x3x3 boolean array and define the cut out areas by true/false

then next step is to use hybridisation, you can exchange the 3x3x3 array at every following iteration,

and can create some fancy rules for what 3x3x3 array should be taken in next iteration, e.g. fill the 3x3x3 array with indexes to another array, every non zero indes is a "cube" in an iteration

... just my 5 cents wink
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divide and conquer - iterate and rule - chaos is No random!
Max Sinister
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« Reply #6 on: May 10, 2016, 08:57:59 PM »

Of course... and that way you could also create, let's say, the Menger Cross. Just by inverting the booleans.

Which software did you use for that? And how did it create graphics, and how did they look like? Are they somewhere here in the forum?
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cKleinhuis
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« Reply #7 on: May 11, 2016, 12:21:01 PM »

no, it was an opengl realtime app, and was used in a pc intro i made 10 years ago wink
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divide and conquer - iterate and rule - chaos is No random!
Max Sinister
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Posts: 114


« Reply #8 on: May 12, 2016, 09:41:31 PM »

Ah, OK.

(Thinking about the last picture: It looks as if the sponge was melting or withering. Bad material? wink)
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