Lmst

Van der Pol Oscillator
#chaos
#instability
#attractor
#Lorentz
#butterfly_effect
Det er fordi det er en smuk måde at forsøge at beskrive det ubeskrivelige på, det som er kaos, og de grafiske sager som kommer siden, efter eller bagved matematikken og en anelse senere i opdagelserne af det kaotisk-matematiske, som bare er så hagetabende smukke....

Inspireret af "daß sensible chaos", schwenk...og flere med mere.( liste her senere);

A very simple way to draw HAKMEM 149 based structures by using whole 32 bits range with upper bits as coordinates using unsigned shifts.

This also works with a lower range but it loses precision.

The oblique version is even simpler by removing the last two operations.

The structure looks like Apollonian net or Hopalong attractors.

This drawing method also works with other attractors or Gingerbread man map etc.

#sizecoding #codegolfing #algorithm #attractor #fractal #computergraphics

HAKMEM 149 based structure produced by the attached code

HAKMEM 149 based structure produced by the shown code with : x -= 1 << 30

simplified p5js code of the HAKMEM 149 structure using 32 bits range with upper bits taken as coordinates, coordinates shifts are adapted to a 512x512 framebuffer.

The X and Y offsets can be modified to show different structures, this can also be simplified by removing the offsets code and initializing X and Y with large values.

For this particular case "y += 1 << 31" is unneeded (produce the same result)

10 years (exactly) on from my unanswered question

"Interior Distnace Estimate for Julia Sets - Getting Rid Of Spots"
https://math.stackexchange.com/questions/1153052/interior-distance-estimate-for-julia-sets-getting-rid-of-spots

I think I found the answer: apply l'Hospital's rule to the limit for attracting (not super-attracting) interior distance, take the maximum of all such distance estimates.

https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule

Not very principled (I haven't checked the necessary conditions for the rule to be valid), but seems to work ok for removing the spots at the preimages of the attractor.

#fractals #JuliaSet #DistanceEstimate #graphics #attractor #PreImage