Dr. Pickover's suggestion

I follow Pickover on twitter, and he made this suggestion today

"A simple formula produces strange and unpredictable forms ⁠— wispy, chaotic ghosts composed of 10 million points. "

here's the link he provided

https://fronkonstin.com/2017/11/07/drawing-10-million-points-with-ggplot-clifford-attractors/

and the formulas are incredibly simple

Among many, many books by Pickover (check on Amazon!), you might like this one with many more examples of chaos and fractal images:

Computers, Pattern, Chaos and Beauty
Clifford A. Pickover
St. Martin's Press
1990

Inexpensive used copies are available online.

Some similar chaotic images can be made using a pixel formula and Latööcarfian Attractors in mt.ucl. Here's an image:

and the upr:

lato {
::LT2D2gn2ViVTvNOOM07Fo/HM89map8ZnF6Qn2pFYw09yOFY39SgitcsmRWyQSppJ/6HaZ70m
  GJ70bOiPSR+EFFZy10ULV8lLvIKyytCGJWQtq4ot8MbBZRSSUBjvuwSmBfKo7YaDBVjOVzy4
  WDJ+78yovK2w+L81zvGngHHf5FOgOjmSrsclkE/j6limEHpqopc7OCCMYJzWoyIlbEWeF1Yu
  8iSaVFXuuRXm0y0kkrBg01y69NXpBwUn4S6r8a5ooKmOtgl+biKPPKnLYSaJEJ/Ssa0m8y4I
  wO6dk4K+rMxvqA/jLN8MWTUrpSTOYGBXyo6IjSwzITwzXgHPuOofzel2RbSFx1a1axS7V10l
  Klqz5UZcU1yyNWqLi/HLVmR1Z1rRflMOB+gSuC82lrIjrNS1yUSyo5ThPy6+QLzISF8hwWoZ
  mCY9xwvMMWGBhHPZ6s5Lu8C1G7hAIjBBDwnjQfmYpz7+YE9ITy080H10MOs0dKhSDnHxt+b7
  PvTAHWtEsY1X++P+6y75Gwkps+0Y0LLX3Yf3p/pS7+dt4A636YDiESUrPFw4kFJoTE3wM7YG
  f6uPbPZ/JrSlrhrHn615A49+MDlggM38Ps6DEDXW4D/DPMA/4A0cGDXDCF5OUbMM9Zh8Naa+
  Yv7Yv+bFBftXTn/8PPO94JFbFfj5Zwv+ZnfFHQzjphwgGMAbgdWcRDUfeJBHWD4s/lTOhdCq
  ZtQaRTc108KCVn0EURsLlynoVJ9p4KEU4Jkm4Qaa3qygb1N1jOWEwQPxlPB11kKfqmlVylEk
  v1BdCcGYOcp+JVmXrW7NHX15f/v/POE0hzjaR1V7igRoE0NhR++iK34HjdXFrP/fkxHf6kwl
  wGYDxoOjLUr9p+BmDFarlIfnGgNRfCCFdeMK68pU05wpoBJVUYWFNMti64VvPGc/5n05wOMH
  1B7M4oWo9zRNg6jjaQ4ljaE1LH1a/hy9wBz9wBy9wfgXvjrTFsgpf4zL9Df+pf4jeAE3jJds
  bj/FAB8WYY1NQ7yM5y2OaD03RD0311rfA6+2oCYl9Ec4o12n266WXDdY11BUY15ylQnpkvxt
  FQv+BoJ12mBI8LOTt0kShtJ81V8no4O+TWiH7rQ/Ag7u41HGzwxzglpwD8GgqktkKEk4obFC
  vXiAKA2hJnsehabJVuL47y1q57OcreY/HobdEjHPtarFGrZq34seUQS2J9U9orL0TgvKUrLp
  u9O+WNkKCDZyTjuFYX6a/FXurJlzXP3mfzhx2eJ4rDvvllTbviLpCyfrkMf6C3Eg75neVdFl
  LqvGh+m/CSaWKvy5PdDD1MtsqsE+GGL7eWOFoxonFQbvRP0MifUH4RxRmSlCmuHKDFpVtjre
  F2dgwlZsXJwoou9kgmhwoFTn2uO6ggJzmeDqdV8bwnO7NjAWsd5FzRzwLqnbtZ2fn/26EQ+R
  D8kD/zA4pgr8H0si0WK=
}

{Anti-aliasing is not useful for chaotic images.)

Thanks to you both. Cool stuff. But when I paste Jim's parameters into UF I get this message (even after updating my formulas):

Ultra Fractal was unable to find ‘pixeljp’ in ‘jlb.ufm’

Thanks to you both. Cool stuff. But when I paste Jim's parameters into UF I get this message (even after updating my formulas):

Ultra Fractal was unable to find ‘pixeljp’ in ‘jlb.ufm’

I get this error too but you just need a plain pixel formula for this to work. UF suggested "pixeljp" in jp.ufm which works just fine.

Thanks Chris. UF Mac didn’t suggest a replacement formula but that one does the job.

I had copied that pixel formula into jlb.ufm, just for convenience, but must have forgotten to upload the file.

I got inspired, so more chaotic attractors coming soon.