dwitter.net | #circleChallenge

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u(t) is called 60 times per second. t: Elapsed time in seconds. S: Shorthand for Math.sin. C: Shorthand for Math.cos. T: Shorthand for Math.tan. R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5) c: A 1920x1080 canvas. x: A 2D context for that canvas.
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  • u/rep_movsd
    I found those by for(N=0.1;N<1;N+=.1) M=(1-N*N)**.5,console.log(N,M)
  • u/rep_movsd
    Can be 67 bytes
  • u/rep_movsd
    Can be 67 bytes
  • u/rep_movsd
    [P,Q]=t?[P*.8+Q*.6,Q*.8-P*.6]:[0,1] x.fillText(0,99*Q+960,99*P+540)

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  • #circlechallenge No trig, no direct square root: Just using the Pythagorean theorem + the fact that sums of odd numbers give perfect squares

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  • As part of #circlechallenge I go back to the old rational parametrization of the circle from Wildberger's "chromogeometry", which has elements of Euclid. Each frame draws rational points on a circle, and each frame the radius gets bigger. All of the patterns are a kind of optical illusion.
  • u/donbright
    changing '2' and '3' to different numbers will give different patterns

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  • u/donbright
    does fillrect have 6 parameters here?
  • u/cantelope
    heh. it only looks at the first 4. i'm not actually saving any space by including 6 parameters, but why not? :)
  • u/cantelope
    can you see how this circle method works? there is an array with 4 elements, the first 2 being positions (x,y), and the last 2 being analogous to a vector (in physics) with magnitude and direction, or simply (velocity-x, velocity-y). The velocity vector is added to the position coordinates once per frame and is itself adjusted in a way to create a perfectly circular "orbit" about the origin. Interestingly, this approach can be extended into 3 or more dimensions, and involve, obviously, more than 2 bodies. 3-body orbital chaos can be very interesting and beautiful, e.g. https://code.dweet.net/full/2w8z

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