### love matrix

LOVE MATRIX by nutsu, a study for drawing curl curve.

```// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(0.85);

// Global code will be evaluated once.
const turtle = new Turtle();
turtle.penup();
////////////////////////////////////////////////////////////////////////////
turtle.quadraticCurveTo = (cx, cy, x1, y1, steps = 20) => {
const s = 1 / steps;
const p = turtle.pos();
const x0 = p[0];
const y0 = p[1];
for (let t = 0; t < 1; t += s) {
turtle.goto(
(1 - t) * (1 - t) * x0 + 2 * (1 - t) * t * cx + t * t * x1,
(1 - t) * (1 - t) * y0 + 2 * (1 - t) * t * cy + t * t * y1
);
}
turtle.goto(x1, y1);
};
////////////////////////////////////////////////////////////////////////////
// LOVE MATRIX by nutsu, a study for drawing curl curve.
class Mat2 {
constructor() {
this.a = 1.0;
this.b = 0.0;
this.c = 0.0;
this.d = 1.0;
this.tx = 0.0;
this.ty = 0.0;
}
static create() {
return new Mat2();
}
multiply(b) {
const aa = this.a, ab = this.b, ac = this.c, ad = this.d;
this.a = aa * b.a + ac * b.b;
this.b = ab * b.a + ad * b.b;
this.c = aa * b.c + ac * b.d;
this.d = ab * b.c + ad * b.d;
this.tx += aa * b.tx + ac * b.ty;
this.ty += ab * b.tx + ad * b.ty;
return this;
}
const aa = this.a, ab = this.b, ac = this.c, ad = this.d;
this.a = aa * c + ac * s;
this.b = ab * c + ad * s;
this.c = aa * -s + ac * c;
this.d = ab * -s + ad * c;
return this;
}
translate(x, y) {
this.tx += this.a * x + this.c * y;
this.ty += this.b * x + this.d * y;
return this;
}
scale(x, y) {
this.a *= x;
this.b *= x;
this.c *= y;
this.d *= y;
return this;
}
}
class WormObject {
constructor(x, y, vx, vy, len) {
this.vmt = Mat2.create().translate(x, y).rotate(Math.atan2(vy, vx));
const angle = (Math.random() * Math.PI / 2) - (Math.PI / 4);
this.tmt = Mat2.create().scale(0.92, 0.92).translate(len, 0).rotate(angle);
this.c1x = this.p1x = -0.5 * this.vmt.c + this.vmt.tx;
this.c1y = this.p1y = -0.5 * this.vmt.d + this.vmt.ty;
this.c2x = this.p2x =  0.5 * this.vmt.c + this.vmt.tx;
this.c2y = this.p2y =  0.5 * this.vmt.d + this.vmt.ty;
this.r = angle;
this.w = len * 0.4;
}
draw() {
if (Math.random() > 0.9) {
this.tmt.rotate(-this.r * 2);
this.r *= -1;
}
this.vmt.multiply(this.tmt);
const cc1x = -this.w * this.vmt.c + this.vmt.tx;
const cc1y = -this.w * this.vmt.d + this.vmt.ty;
const pp1x = (this.c1x + cc1x) / 2;
const pp1y = (this.c1y + cc1y) / 2;
const cc2x = this.w * this.vmt.c + this.vmt.tx;
const cc2y = this.w * this.vmt.d + this.vmt.ty;
const pp2x = (this.c2x + cc2x) / 2;
const pp2y = (this.c2y + cc2y) / 2;
turtle.goto(this.p1x, this.p1y);
turtle.down();
turtle.goto(pp2x, pp2y);
turtle.up();
this.c1x = cc1x;
this.c1y = cc1y;
this.p1x = pp1x;
this.p1y = pp1y;
this.c2x = cc2x;
this.c2y = cc2y;
this.p2x = pp2x;
this.p2y = pp2y;
}
}
// The walk function will be called until it returns false.
let px = 0, py = -20;
function walk(i) {
const t = i / 20;
const x = 4 * (16 * Math.pow(Math.sin(t), 3));
const y = -4 * (13 * Math.cos(t) - 5 * Math.cos(2 * t) - 2 * Math.cos(3 * t) - Math.cos(4 * t));
const vx = x - px;
const vy = y - py;
px = x;
py = y;
let len = 1.3 * Math.sqrt(vx * vx + vy * vy);
if (Math.random() > 0.95) len *= 2;
const o = new WormObject(x, y, -vx, -vy, len);
for (let j = 0; j < 50; j++) {
const x = o.vmt.a * o.vmt.a + o.vmt.b * o.vmt.b;
if (x * o.w < 0.02) break;
o.draw();
}
return i < 120;
}
```