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Going back to one of my oldest creations, I discovered today that it produces some nice Julia set images.

The formula is as follows:

  if (z*z>x*x) {d=z;z=x;x=d;}
  if (y*y>x*x) {d=y;y=x;x=d;}
  if (z*z>y*y) {d=z;z=y;y=d;}

 <standard quaternion (no 4th dimension term)>

 x=x+a;y=y+b;z=z+c; where (a,b,c) is a constant seed value.

(http://www.fractalforums.com/gallery/2/803_28_06_10_1_13_37.png)
(http://www.fractalforums.com/gallery/2/803_28_06_10_1_11_44.jpeg)
(http://www.fractalforums.com/gallery/2/803_28_06_10_1_10_05.jpeg)
(http://www.fractalforums.com/gallery/2/803_28_06_10_1_07_19.png)
(http://www.fractalforums.com/gallery/2/803_28_06_10_3_13_50.png)

msltoe:

  I'm going to try a breed of that formula with Tom Lowe's box and a few other things.  Very.. interesting.  Nice to have a new angle to pursue.

Maybe i implemented it wrong, is there the "y,z = 0 must have" issue for the julias again?
For x variants it worked so far:

...and a combination with your "fuzzy" formula:

(http://www.fractalforums.com/gallery/2/1127_29_06_10_4_01_08.jpeg)

WOW, beautiful Jesse!!

Very viral  O0

It's a fractal code :D What happens if you interpret those "dots" as binary data? xD

Jesse: Good ones. b and c can be non-zero. You'll still get discontinuities but also some good variations. I dial up the iterations which tends to hide the discontinuities, but makes the objects more difficult to render.

Oooooooo ... shiny \o/

That is a very good hint Msltoe, thanks!  Increasing the minimum iteration count removes the spread pixels mostly.
The alternative way would be a double check feature in the DE, but in the 4 point method i would have to add 3 whole iterations, what  slows it to much down.

Another variation on the formula: a maximum clip on the Z value can also give some nice structures.

Flipping only the x and y coordinates yields a "fractal frog" (-0.8,-0.1,+0.1):
(http://www.fractalforums.com/gallery/2/803_01_07_10_3_03_18.png)

very stylized frog but definitely a great one :D

I guess that's what a bufo alvarius may possibly look like after one has smoked its "milk"...

 O0

As Jesse alluded to in his z-plane cutoff comment, more secrets lie in the interior of these xyz rocks:

(http://www.fractalforums.com/gallery/3/803_02_08_10_3_44_21.jpeg)
(http://www.fractalforums.com/gallery/3/803_02_08_10_3_26_50.jpeg)

wow, cool!

Whoah. We need to view these in 4 dimensions, so that we can see all of the interior as well. :)

4D eyes projecting the light onto their 3D retina surface... that would be amazing :D
And certainly the best way to view those :)

I wondered if in 4D you would have 3D-table surfaces where you basically lie something onto that surface and it stays there. As if you put a 3D object onto a 2D-surface.

Those sections are amazing :D

That looks really cool, nice way to cut off the bulb!

What i meant in my previous post was to clip the Z value in the iteration loop, however your idea is better  :dink:

Wow, these are great pictures!
More please :-)

Thanks for the compliments. It also helps that I now use a min(norm) coloring scheme which brings out the patterns.
Here's one more with alternating seeds (-0.8,0,0) and (-1.2,0,0):
(http://www.fractalforums.com/gallery/3/803_05_08_10_3_27_27.jpeg)