Chooses 3-5 prime factors, then at each iteration, turns right if `i` is not divisible by any of the factors, left otherwise. A completely symmetric draw of a pattern takes `4 × (the product of the chosen primes)` iterations.
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Canvas.setpenopacity(-0.5);
const size = 0.75;
const steps = 4;
const extent = 100;
const start = [0, 0];
const primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61];
Turtle.prototype.checkBounds = function() {
this.penup();
const x = this.x();
const y = this.y();
if (x > extent) this.setx(-extent+(x-extent));
else if (x < -extent) this.setx(extent-(-1*(x+extent)));
if (y > extent) this.sety(-extent+(y-extent));
else if (y < -extent) this.sety(extent-(-1*(y+extent)));
this.pendown();
}
Turtle.prototype.decideDirection = function(i) {
return this.factors.reduce((a, f) => a && i%f, true);
}
Turtle.prototype.chooseFactors = function(factors) {
const n = 3+Math.floor(2*Math.random());
this.factors = [];
for (let i = 0; i < n; i++) {
this.factors.push(factors.splice(Math.floor(Math.random()*factors.length), 1));
}
}
const turtle = new Turtle();
turtle.penup();
turtle.goto(start[0], start[1]);
turtle.chooseFactors(primes);
turtle.end = turtle.factors.reduce((a, f) => a*f, 4);
turtle.pendown();
function walk(i) {
turtle.circle(turtle.decideDirection(i) ? size : -size, 90, steps);
turtle.checkBounds();
return i < turtle.end;
}