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#mandelbrotset

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freedosproject
The FreeDOS Project @freedosproject@fosstodon.org · Aug 03, 2026
Here's something fun to try on FreeDOS! Use Open Watcom FORTRAN77 with the graphics extensions to draw the #MandelbrotSet #fractal https://www.both.org/?p=14481
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mathr
claude @mathr@post.lurk.org · Jul 26, 2026

what if... one could construct a low precision #MandelbrotSet orbit corresponding to a specific high precision orbit, without doing any high precision calculations?

I'm experimenting with constructing "tuned" periodic orbits by a simple algorithm (cycle one orbit, replacing the periodic 0 with successive values from a second orbit; scaled by Julia size of the first orbit, then iterate backwards with Newton's method to fix it up to be less approximate)

seems to work in some simple cases, in other cases the refinement pushes it to a wrong orbit*, so I think my initialization is wrong. plotting the images after each step of Newton refinement shows it takes some bonkers path instead of moving smoothly from the approximate to the accurate....

  • e.g. in attached video I specified to go to the same side relative to the mini each time, but it doesn't do that...

#maths

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