Schramm–Loewner evolution by Tesseract

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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Tesseract

function u(t) {

n=c.width=133
d=(a,b)=>[a+(o=a-7-C(t))*(k=.1/(o*o+b*b)),b-b*k]
for(l=1e4;l--;)x.fillRect(j=l%n,i=l/n,1,(C[l]=t?d(...C[l]):[i/5,j/5])[1])

Oct 30 2020 12:38 PM UTC

}// 136/140

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Schramm–Loewner evolution

u/Tesseract

If anyone knows how to get something that looks like brownian motion as a function of t in around 10 bytes, I'd like to know (it should replace C(t)).
u/rodrigo.siqueira

maybe C(t*i**8) is more random
u/rodrigo.siqueira

I see a very beautiful orange SLE (Schramm-Loewner Evolutions) here: http://www.statslab.cam.ac.uk/~jpmiller/teac… I wish this could be reproduced in javascript.
u/rodrigo.siqueira

I asked jpmiller about how he did that incredible beautiful orange SLE and got his answer, if you want to reproduce it The way that the image was made is using the following steps: "1) Sample an instance of the Gaussian free field (GFF) — see Page 24 of this paper for Mathematica code which produces it https://arxiv.org/pdf/math/0312099.pdf 2) The GFF is a function h defined on the grid {1,...,n}^2. If you consider its exponential exp(i c h), where i = sqrt(-1), c > 0 is a constant, then you get a vector field. 3) Then you can consider flow lines of this vector field by solving the equation eta’(t) = exp(i c h(eta (t)). The image essentially shows flow lines with angles +/- pi/2 starting from every point in the square where c = 1 / (2/Sqrt(128) + Sqrt(128)/2) — this is the value of c so that what you will see will be related to SLE with kappa = 128. Best wishes, Jason"


      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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