This is the bare minimal code necessary to produce Mandelbrot set from scratch without using external libraries or complex numbers (written in both JavaScript and Python).
The following educational video provides the code walkthrough and illustrates it is relevance to Wolfram's Physics Project: https://youtu.be/mzizK6ms-gY
<canvas id="gardun" width="1000" height="1000"></canvas>
<script>
m = document.getElementById("gardun").getContext("2d")
atom = function(x,y,c){m.fillStyle=c; m.fillRect(x,y,3,3)}
for(y=1; y<1000; y++){
for(x=1; x<1000; x++){
dx = (x-500)/2000-0.12
dy = (y-500)/2000-0.82
a = dx
b = dy
for(t=1; t<200; t++){
d = (a*a)-(b*b)+dx
b = 2*(a*b)+dy
a = d
H = d>200
if(H){atom(x,y,"rgb("+ t*3 +","+ t +","+ t*0.5 +")"); break}
}}}
</script>