Formula 21 (Julia Set Interpretation)

[trafassel]

<a href="http://www.youtube.com/v/HbUFgdbDIiI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/HbUFgdbDIiI&rel=1&fs=1&hd=1</a>

for (n = 1; n < zkl; n++) {

   ai = 2 * ai * ar * aj + bi;
   aj = aaj - (aai + aar) / 2.0 +  bj;
   ar = aar - (aai + aaj) / 2.0 + br;
   aar = ar * ar; aai = ai * ai; aaj = aj * aj;
   d = aar + aai + aaj;
   if ((d) > gr) { tw = n; break; }

}

On the first part of the Video bi=bj=br=0.

[trafassel]

Ups, the pictures are from the "1000 iterations" thread.

[kram1032]

A really nice Julia-animation I like it a lot!

[trafassel]

Same Julia dressed in red and blue.

[trafassel]

Some Variants

[trafassel]

Formula 21 (Ide's Fractal) has some nice properties. Easy formula (only multiplication, addition and subtraction), repeating patterns at high zoom level and some nice parameters to play with. I's not a candidate for a "true 3d mandelbrot" (how could it? It only looks nice as julia), but definitely promising. I like it.

<a href="http://www.youtube.com/v/0YEzdfOt1QU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/0YEzdfOt1QU&rel=1&fs=1&hd=1</a>

(Rendered with Gestaltlupe).

[kram1032]

really nice but:
This is already the second video in short time featuring swan lake. It's a great song and it fits very well but if there is a third one, it'll start to seem overused

[trafassel]

Cool,

this means, next time you want my 8 Bit Style music - created on C64 or Nintendo DS.

[kram1032]

lol, well if it fits the fractal

Maybe something that looks like a bunch of 3Dpixels?

[trafassel]

Scene with 2,4,5 and 8000 iterations.

[trafassel]

3 iterations

[trafassel]

Das totale Miszverständnis:

<a href="http://www.youtube.com/v/ZUuLdcHDwgw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/ZUuLdcHDwgw&rel=1&fs=1&hd=1</a>

[trafassel]

I found an interesting detail in the corresponding mandelbrot variant.