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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > IFS - Iterated Function Systems > KIFS and the "fold and cut problem"
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Author Topic: KIFS and the "fold and cut problem"  (Read 6864 times)
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knighty
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« on: May 21, 2011, 08:47:36 PM »
I realized recently that there is a conection between KIFS and the "fold and cut problem". Basically, KIFS is an iterative application of that technique. Also, the foldings used with KIFS so far are really simple. There are other types of linear foldings that are already used in Origami and kirigami that have 3D (and nD) counterpart. I haven't tried them yet. Hopefully someone will be faster than me at this  grin.
Here are attached some fragmentarium scripts in order to illustrate the idea.
* Fold_and_cut_polyhedra_examples.zip (5.25 KB - downloaded 432 times.)
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Syntopia
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« Reply #1 on: May 22, 2011, 12:41:56 AM »
Interesting!

I made a few examples - it seems stellation occurs a lot.
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KRAFTWERK
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« Reply #2 on: May 22, 2011, 07:53:36 AM »
Cool idea Knighty and beautiful renders I like to zoom into that second image.  A Beer Cup
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #3 on: May 22, 2011, 10:57:13 AM »
Leonardo da Vinci; Icosahedron drawing cheesy



Anyway those images look interesting but don't seem to show fractal detail, why? undecided
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Syntopia
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« Reply #4 on: May 22, 2011, 12:32:47 PM »
Quote from: DarkBeam on May 22, 2011, 10:57:13 AM
Leonardo da Vinci; Icosahedron drawing cheesy

It seems a bit truncated :-)

Quote from: DarkBeam on May 22, 2011, 10:57:13 AM
Anyway those images look interesting but don't seem to show fractal detail, why? undecided

I made them with a low (n=2-3) iteration count. For some parameter choices the structures turn to dust when the iteration count is raised, but it possible to find structures that converge into something solid (like the old KIFS). I'll post a few images if I get some time to explore the system.
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knighty
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« Reply #5 on: May 22, 2011, 02:40:25 PM »
Quote from: Syntopia on May 22, 2011, 12:32:47 PM
Quote from: DarkBeam on May 22, 2011, 10:57:13 AM
Anyway those images look interesting but don't seem to show fractal detail, why? undecided

I made them with a low (n=2-3) iteration count. For some parameter choices the structures turn to dust when the iteration count is raised, but it possible to find structures that converge into something solid (like the old KIFS). I'll post a few images if I get some time to explore the system.
Exactly. Also, depending on the combinations of the DEs at different scales you can get more than KIFS.
Thank you all for your interest. grin
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