A transition from x*x+y*y (the Blue geo… by donbright

function u(t) {

c.width=1920 // clear the canvas
for(i=0;i<9;i++)
x.fillRect(400+i*100+S(t)*300,400,50,200) // draw 50x200 rects

} // 122/140

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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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donbright

remix of d/479 by u/lionleaf

function u(t) {

c.width=256;for(i=128;i--;)for(j=128;j--;){c=i*i+S(t)*j*j;c=(c<0?-c:c)%128;x.fillStyle=R(S(t+3.1)*c+c,0,S(t)*c+c);x.fillRect(64+i,8+j,1,1)}

Mar 4 2017 7:17 AM UTC

}// 140/140

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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)


      u(t) is called 60 times per second.
      t: elapsed time in seconds.
      c: A 1920x1080 canvas.
      x: A 2D context for that canvas.
      S: Math.sin
      C: Math.cos
      T: Math.tan
      R: Generates rgba-strings, ex.: R(255, 255, 255, 0.5)

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