I found an interesting and visually pleasing phenomenon called Domain Coloring. Based on mathematical formulas, I don't know how closely it relates to fractals. I'm a big fan of rainbow coloring and when I stumbled upon these images I was mesmerized. Is there any way to make something like this in UF?
Here's a link: https://www.dynamicmath.xyz/domain-coloring/dcgallery.html

63c0c12a46e14.jpg
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I found an interesting and visually pleasing phenomenon called Domain Coloring. Based on mathematical formulas, I don't know how closely it relates to fractals. I'm a big fan of rainbow coloring and when I stumbled upon these images I was mesmerized. Is there any way to make something like this in UF? Here's a link: https://www.dynamicmath.xyz/domain-coloring/dcgallery.html ![63c0c12a46e14.jpg](serve/attachment&path=63c0c12a46e14.jpg) ![63c0c13d4f35d.jpg](serve/attachment&path=63c0c13d4f35d.jpg) ![63c0c13d4fc23.jpg](serve/attachment&path=63c0c13d4fc23.jpg) ![63c0c13d51b92.jpg](serve/attachment&path=63c0c13d51b92.jpg)
 
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Yes, UF can absolutely do this, and I wouldn't be surprised if it's already implemented somewhere in the jungle of public coloring algorithms. If not, it should be relatively easy (compared to what other CAs do) to implement this.

The simplest way would be to:

  1. use a fractal formula that does nothing (just bails out after 0 iterations)
  2. use a coloring algorithm that assigns color based on real and imaginary value (direct coloring algorithm)
  3. use whichever function you'd like to examine as a mapping
Yes, UF can absolutely do this, and I wouldn't be surprised if it's already implemented somewhere in the jungle of public coloring algorithms. If not, it should be relatively easy (compared to what other CAs do) to implement this. The simplest way would be to: 1. use a fractal formula that does nothing (just bails out after 0 iterations) 2. use a coloring algorithm that assigns color based on real and imaginary value (direct coloring algorithm) 3. use whichever function you'd like to examine as a mapping
edited Jan 13 at 9:17 am
 
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Thank you very much for your response Phillip, appreciate the feedback. I'm vague on Direct Coloring formulas...is this the same as Direct Orbit Traps? Every time I try to use it the colors seem so dull. What are some examples of Direct Coloring formulas?

Thank you very much for your response Phillip, appreciate the feedback. I'm vague on Direct Coloring formulas...is this the same as Direct Orbit Traps? Every time I try to use it the colors seem so dull. What are some examples of Direct Coloring formulas?
 
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Direct Orbit Traps is a direct coloring algorithm, the difference is merely that a coloring algorithm returns an index for a color in the selected gradient whereas a direct coloring algorithm returns an RGB triplet. To achieve the nice coloring shown in your example you will probably need to work in HSV (hue, saturation, value) space, there are conversion formulas to be found online between the two color spaces.

Direct Orbit Traps is a direct coloring algorithm, the difference is merely that a coloring algorithm returns an index for a color in the selected gradient whereas a direct coloring algorithm returns an RGB triplet. To achieve the nice coloring shown in your example you will probably need to work in HSV (hue, saturation, value) space, there are conversion formulas to be found online between the two color spaces.
 
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It reminds me of Carlson Orbit Traps:

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It reminds me of Carlson Orbit Traps: Fractal1 { ::MefPghn2NyZWPyNOSC43Ng/PUwvP28mU7g8hpnBexsYc7G2enG7+ihqKV5SdpUZ2KV6j9X/G 8U8SSuBmBuE1HZE8IYEBZqHnafYud4/4lv4u7m7nH6O8q3afE+V39t+jzPdALJo7eqr/LPNf ATaQ3N0+juprHwamHm6O2PfVT1dsbq/57+4Q/f8c30p2x/K+NY2bIIC9V31OO33O03etf8LH +R31X+CTtYa3HavM3fe8wr+l2He+LTnvNe8V3d+S7D9z/4AGhu7U38TnPeYofsrd6u5p2xrX an6Gnt10p2LXgq1WXwT7mO8XQvWiU0GBChE43geNlTlEJhSlN87O1+lRQVow7wpsX+iHPPd6 2QrpCO1+9edNQ4o7esfobs9E0n8x52xjtTHf9tHP9q7g2Y6HHe17gn1Nc/055Xd3lPfduda+ A6NIdtc5zXO/Ndt8GE8vvvtf48Ndvn6lvof8a/xObHuWTeEetxzjdv8FwrUWkTpXElnf4B6r v9wQQMgH8X+7tTDXPP++p77n/0U7lrvyKFz6/9/GGt09vUKy9oP9jLdH+lb3f/Q3V3je35j6 x++prz39PhOgW9QirWaH/yQ3bvN+A+j9/fdHQvGn8w3dbYu/yQPItm5EPGVm+/TXT4DgmNOX tMitss2iUrtI5t1lP/H3gpVfsr7I8u0GqkDj2YhSyjbLSucc5zwA9H6aHOwsVz9tDDuWko/z hz3f9DtH7vdV/Eu/RRtP61cHqugfzMeDPT/ATPbk8Dt1/7BmeSyl+pWf7Qt42n97m1awD18d tHfLsI8MMRWjfs/0lhujf8yTdTn7P6rYL+jDdfPS4xRPKI/YtU9EMHp7Pv1PmyHeckqRSedb fLm/G8rJ6OW7YcocfXbon9pfc5sXdwu/2pOhW9S3cbsIb+73/4jX7mjfyf/8w5JtJD6/Aek+ 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Ultra Fractal author

 
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Here's another link in support of the Domain Coloring idea with an interesting collection of pics, my favorite one is the first. The white lines are cool. And down the page look to be some Ducky fractals, go figure! http://blog.hvidtfeldts.net/index.php/2012/03/lifted-domain-coloring/

Here's another link in support of the Domain Coloring idea with an interesting collection of pics, my favorite one is the first. The white lines are cool. And down the page look to be some Ducky fractals, go figure! http://blog.hvidtfeldts.net/index.php/2012/03/lifted-domain-coloring/
 
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Very nice Frederik, thank you! I love Carlson orbit traps, kcc coloring. It is one of my favorites for sure with the beautiful bright colors. One thing I didn't realize is that it actually says Direct Coloring underneath:
63c2ba731d1e2.jpg

Looks like Paul Carlson also did a study on Newton M-set fractals found here:
https://www.semanticscholar.org/paper/Two-artistic-orbit-trap-rendering-methods-for-M-set-Carlson/0341ad367379fba0700bbd2fde485fa4689c8d40

Very neat pics! You can do a lot with the Newton formula with so many variations. I just don't know how he captured the Mandelbrot set in the middle of these.

Very nice Frederik, thank you! I love Carlson orbit traps, kcc coloring. It is one of my favorites for sure with the beautiful bright colors. One thing I didn't realize is that it actually says Direct Coloring underneath: ![63c2ba731d1e2.jpg](serve/attachment&path=63c2ba731d1e2.jpg) Looks like Paul Carlson also did a study on Newton M-set fractals found here: https://www.semanticscholar.org/paper/Two-artistic-orbit-trap-rendering-methods-for-M-set-Carlson/0341ad367379fba0700bbd2fde485fa4689c8d40 Very neat pics! You can do a lot with the Newton formula with so many variations. I just don't know how he captured the Mandelbrot set in the middle of these.
 
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