Exploration of the XYZ-symmetrized quaternion julia set

[msltoe]

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.

[M Benesi]

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.

[Jesse]

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:

[Jesse]

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

[KRAFTWERK]

WOW, beautiful Jesse!!

Very viral 

[kram1032]

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

[msltoe]

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.

[ker2x]

Oooooooo ... shiny \o/

[Jesse]

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.

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.

[msltoe]

Flipping only the x and y coordinates yields a "fractal frog" (-0.8,-0.1,+0.1):

[kram1032]

very stylized frog but definitely a great one

[blob]

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

 

[msltoe]

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

[cKleinhuis]

wow, cool!

[hobold]

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