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Author Topic: Kaleidoscopic (escape time) IFS  (Read 63006 times)
Description: An interresing class of fractals
0 Members and 2 Guests are viewing this topic.
PhotoComix
Strange Attractor
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Posts: 276


« Reply #135 on: July 04, 2012, 10:48:01 AM »

really a long topic, but i couldn't find the answer to my question :

there is a practical implementation a formula that may be used in M3D, for kaleidoscope IFS ?
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DarkBeam
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Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #136 on: July 04, 2012, 05:08:08 PM »

Guess what? Sierpinski3, Menger3, MengerIFS, Dodecahedron, Icosahedron, Octahedron tease ... All of them are KIFS!!!
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No sweat, guardian of wisdom!
PhotoComix
Strange Attractor
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Posts: 276


« Reply #137 on: July 04, 2012, 08:30:42 PM »

wow! cheesy
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Clemensson
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Posts: 2


« Reply #138 on: October 28, 2013, 10:23:48 PM »

Hi Kaleidos!

So i made this small Dx11 fractal renderer for a course at my university, which is called 'Fractals" cheesy

Anyways the idea was to simply generate new Kaleidoscopic Fractals with a few cklicks. In other words: add operators, modify the scaling, change parameters on the fly. Its not something new in terms of Fractal Theory but i thought it might be cool to have a tool to fool around with math.

And actually after some (very simply) fooling around i came along those following monsters which are all named by my girlfriend and hopefully you guys have not already found them:

Devil-hedron:



Simple extension of the Sierpinski Tetrahedron with a Sphere Fold (as in the Mandelbox). I think its nice because it not only contains itself and
the formula looks something like:
Code:
scale: 2
offset: -1 -1 -1
plane fold 1: 0.71 0.71 0
plane fold 2: 0.71 0 0.71
plane fold 3: 0 0.71 0.71
sphere fold: 0.25 1.00

Moonflake



Well this is essentially the Koch Snowflake with a Sphere Fold (see the pattern here?). It actually gives the former flat fractal a body with a copy of itself at the pointy end smiley
the formula looks something like:
Code:
scale: 2.5
offset: -2 -1 0
plane fold 1: 0.71 -0.71 0
plane fold 2: 0.71 0 -0.71
plane fold 3: 0 0.71 -0.71
sphere fold: 0.25 1.00

P.S.: again if those are already know, i am sry and i wont take credit for it, just let me know smiley
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