### Hexagon Fractal

Spawning hexagons recursively.

#hexagon #fractal

```const turtle = new Turtle();
const maxDepth = 6; // min=1, max=10, step=1
const splitChance = 0.8; //min=0, max=1, step=0.001
const addHatching = 1; // min=0, max=1, step=1 (No, Yes)
const firstCubeSize = 140; // min=1, max=200, step=0.5

const polys = new Polygons();

class Hexagon {
this.center = center;
this.positive = positive;
this.depth = depth;

this.points = [this.center];
for (let i=0; i<6; i++) {
}
}
getPolygons() {
const p = this.points;
if (this.positive) {
return [[p[1],p[2],p[0],p[6]], [p[0],p[2],p[3],p[4]], [p[0],p[4],p[5],p[6]]];
} else {
return [[p[0],p[3],p[4],p[5]], [p[1],p[0],p[5],p[6]], [p[1],p[2],p[3],p[0]]];
}
}
getSpawnPoints() {
const p = this.points, r = this.radius, d = this.depth;
if (this.positive) {
return [{center: p[1], depth: d+1, positive: true, radius: r / 2},
{center: p[3], depth: d+1, positive: true, radius: r / 2},
{center: p[5], depth: d+1, positive: true, radius: r / 2},
{center: p[0], depth: d+1, positive: false, radius: r / 2}];
} else {
return [{center: p[2], depth: d+1, positive: false, radius: r / 2},
{center: p[4], depth: d+1, positive: false, radius: r / 2},
{center: p[6], depth: d+1, positive: false, radius: r / 2},
{center: p[0], depth: d+1, positive: true, radius: r / 2}];
}
}
}

const hexagon = new Hexagon([0,0], firstCubeSize, true, 0);
const hexagons = [];
const pool = [hexagon];

do {
const h = pool.shift();
hexagons.push(h);

const spawn = h.getSpawnPoints();
spawn.forEach(p => {
if (p.depth < maxDepth && (Math.random() < splitChance / (1 + p.depth*0.05) || p.depth < 2)) {
}
});
} while(pool.length);

hexagons.reverse();

// The walk function will be called until it returns false.
function walk(i) {
const ps = hexagons[i].getPolygons();

ps.forEach((p, i) => {
const poly = polys.create();
}

polys.draw(turtle, poly);
})
return i < hexagons.length - 1;
}

//
// 2D Vector math
//

function cross(a, b) { return a[0]*b[1]-a[1]*b[0]; }
function equal(a,b) { return .001>dist_sqr(a,b); }
function scale(a,b) { return [a[0]*b,a[1]*b]; }
function add(a,b) { return [a[0]+b[0],a[1]+b[1]]; }
function sub(a,b) { return [a[0]-b[0],a[1]-b[1]]; }
function dot(a,b) { return a[0]*b[0]+a[1]*b[1]; }
function dist_sqr(a,b) { return (a[0]-b[0])**2+(a[1]-b[1])**2; }
function dist(a,b) { return Math.sqrt(dist_sqr(a,b)); }
function length(a) { return Math.sqrt(dot(a,a)); }
function normalize(a) { return scale(a, 1/length(a)); }
function lerp(a,b,t) { return [a[0]*(1-t)+b[0]*t,a[1]*(1-t)+b[1]*t]; }
function rotate(v, center, angle) {
const x = v[0] - center[0], y = v[1] - center[1];
return [x * Math.cos(angle) - y * Math.sin(angle) + center[0], x * Math.sin(angle) + y * Math.cos(angle) + center[1]];
}

////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////

function Polygons() {
const polygonList = [];
const Polygon = class {
constructor() {
this.cp = [];       // clip path: array of [x,y] pairs
this.dp = [];       // 2d lines [x0,y0],[x1,y1] to draw
this.aabb = [];     // AABB bounding box
}
// add point to clip path and update bounding box
let xmin = 1e5, xmax = -1e5, ymin = 1e5, ymax = -1e5;
(this.cp = [...this.cp, ...points]).forEach( p => {
xmin = Math.min(xmin, p[0]), xmax = Math.max(xmax, p[0]);
ymin = Math.min(ymin, p[1]), ymax = Math.max(ymax, p[1]);
});
this.aabb = [(xmin+xmax)/2, (ymin+ymax)/2, (xmax-xmin)/2, (ymax-ymin)/2];
}
// add segments (each a pair of points)
points.forEach(p => this.dp.push(p));
}
for (let i = 0, l = this.cp.length; i < l; i++) {
this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
}
}
draw(t) {
for (let i = 0, l = this.dp.length; i < l; i+=2) {
t.jump(this.dp[i]), t.goto(this.dp[i + 1]);
}
}
const tp = new Polygon();
tp.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);
const dx = Math.sin(a) * d,   dy = Math.cos(a) * d;
const cx = Math.sin(a) * 200, cy = Math.cos(a) * 200;
for (let i = 0.5; i < 150 / d; i++) {
tp.dp.push([dx * i + cy,   dy * i - cx], [dx * i - cy,   dy * i + cx]);
tp.dp.push([-dx * i + cy, -dy * i - cx], [-dx * i - cy, -dy * i + cx]);
}
tp.boolean(this, false);
this.dp = [...this.dp, ...tp.dp];
}
inside(p) {
let int = 0; // find number of i ntersection points from p to far away
for (let i = 0, l = this.cp.length; i < l; i++) {
if (this.segment_intersect(p, [0.1, -1000], this.cp[i], this.cp[(i + 1) % l])) {
int++;
}
}
return int & 1; // if even your outside
}
boolean(p, diff = true) {
// bouding box optimization by ge1doot.
if (Math.abs(this.aabb[0] - p.aabb[0]) - (p.aabb[2] + this.aabb[2]) >= 0 &&
Math.abs(this.aabb[1] - p.aabb[1]) - (p.aabb[3] + this.aabb[3]) >= 0) return this.dp.length > 0;

// polygon diff algorithm (narrow phase)
const ndp = [];
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const ls0 = this.dp[i];
const ls1 = this.dp[i + 1];
// find all intersections with clip path
const int = [];
for (let j = 0, cl = p.cp.length; j < cl; j++) {
const pint = this.segment_intersect(ls0, ls1, p.cp[j], p.cp[(j + 1) % cl]);
if (pint !== false) {
int.push(pint);
}
}
if (int.length === 0) {
// 0 intersections, inside or outside?
if (diff === !p.inside(ls0)) {
ndp.push(ls0, ls1);
}
} else {
int.push(ls0, ls1);
// order intersection points on line ls.p1 to ls.p2
const cmpx = ls1[0] - ls0[0];
const cmpy = ls1[1] - ls0[1];
int.sort( (a,b) =>  (a[0] - ls0[0]) * cmpx + (a[1] - ls0[1]) * cmpy -
(b[0] - ls0[0]) * cmpx - (b[1] - ls0[1]) * cmpy);

for (let j = 0; j < int.length - 1; j++) {
if ((int[j][0] - int[j+1][0])**2 + (int[j][1] - int[j+1][1])**2 >= 0.001) {
if (diff === !p.inside([(int[j][0]+int[j+1][0])/2,(int[j][1]+int[j+1][1])/2])) {
ndp.push(int[j], int[j+1]);
}
}
}
}
}
return (this.dp = ndp).length > 0;
}
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
segment_intersect(l1p1, l1p2, l2p1, l2p2) {
const d   = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]);
if (d === 0) return false;
const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]);
const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]);
const ua = n_a / d;
const ub = n_b / d;
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
return [l1p1[0] + ua * (l1p2[0] - l1p1[0]), l1p1[1] + ua * (l1p2[1] - l1p1[1])];
}
return false;
}
};
return {
list: () => polygonList,
create: () => new Polygon(),
draw: (turtle, p, addToVisList=true) => {
for (let j = 0; j < polygonList.length && p.boolean(polygonList[j]); j++);
p.draw(turtle);