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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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remix of d/479 by u/lionleaf

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  • A transition from x*x+y*y (the Blue geometry, circles) to x*x-y*y (the Red geometry, hyperbolas). This shows a linkage between Binary Quadratic Forms and the Circles and Squares pseudo Fractal / Moiré pattern. By transitioning between two different Binary Quadratic Forms slowly, I hoped to show that the forms themselves are what form these patterns, not simply circles or hyperbolas or trig functions. Inspiration from many dweets on this site and Wildberger's Chromogeometry.
  • u/donbright
    Binary Quadratic Forms are where you take any combination of x*x, y*y, and 2*x*y, for example 3*x*x+2*y*y (an ellipse), of x*x-y*y/2 (a squished hyperbola)

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  • This shows the pattern traced by a line directly between the Earth and Venus as they orbit the sun. This pattern is pretty ancient, for example discussed in the book Quadrivum about the old academic relationships between art and science. This type of pattern may be helpful to appreciate the concept of Orbital Resonance in a planetary system.

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  • a nice clean and simple Sierpinski gasket using XOR + AND
  • u/donbright
    you can increase w to get a bigger pic but it becomes slow

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  • free speech flag! tested ok on firefox/chrome, fonts may disturb other browsers

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  • snowflakes

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remix of d/1283 by u/sfz

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  • Basic Unicode Chinese Character block 4E00–9FFF, (this is not all Chinese characters!). Progress bar on the left.

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remix of d/1232 by u/iverjo

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  • u/iverjo
    Nice :) Better colors than mine
  • u/iverjo
    By saving golfing 2 characters I managed to make the twister bigger:
  • u/iverjo
    c.width=a=2e3;for(i=2*a;i--;)p=S(t)*i/a+i%4/.637,d=C(p)-S(p),d>0&&x.fillRect(a/2+199*(S(p)+S(t)),i/4,199*d,1/(d+1)),x.fillStyle=R(i/9,d*a/8)
  • u/iverjo
    A little more movement: c.width=a=2e3;for(i=2*a;i--;)d=C(p=S(t)*i/a+i%4/.637)-S(p),d>0&&x.fillRect(a/2+199*S(p)+399*C(t),i/4,199*d,1/(d+1)),x.fillStyle=R(i/9,d*a/8)
  • u/donbright
    wow that is awesome!!! i really do miss how yours spins all the way around.
  • u/donbright
    #twister

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remix of d/1055 by u/paberr

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  • stalemate!

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remix of d/869 by u/maysick

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  • just adding color to @maysick 's beautiful spiral

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  • slow burning. more fun with rational paramterization of circles

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