Growing tree.
Export to GIF to see it grow.
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// LL 2021
const spawn_rate = 11; // min=1 max=50 step=1
const thickness = 0.2; // min=0.001 max=0.5 step=0.001
const max_life = 333; // min=1 max=500 step=1
const seed = 0; // min=0 max=100 step=1
const gravity = 0.1; // min=0 max=1 step=0.001
const variation = 90; // min=0 max=100 step=1
const max_variation = variation ? 1 / Math.pow(101-variation, 2.5) : 0;
const offset_y = 90;
const scale = 20; // min=1 max=50 step=1
const style = 2; // min=0 max=3 step=1 (Circles,Lines,Polygons (fast),Polygons (slow))
const circle_fill = 1; // min=0.05 max=1 step=0.05
const max_iterations = 1000;
const draw_hatching = Math.random() < 0.5;
var max_life_t = max_life;
var new_particles = [];
var particles_to_draw = [];
Canvas.setpenopacity(1);
const turtle = new Turtle();
console.clear();
var polygons = null;
class Particle {
constructor(x, y, px, py, radius, current_life, spawn) {
this.x = x;
this.y = y;
this.px = px;
this.py = py;
this.radius = radius;
this.current_life = current_life;
this.spawn = spawn;
this.rng_move = new RNG(seed*(39+current_life));
this.rng_spawn = new RNG(seed*(95+current_life));
}
dup() {
return new Particle(this.x, this.y, this.px, this.py, this.radius, this.current_life, this.spawn);
}
getDrawRadius() {
return this.radius * Math.pow((1 - this.current_life / max_life_t), 2);
}
draw() {
if (style == 0) {
const radius = this.getDrawRadius();
turtle.jump(this.x * scale, (this.y-radius) * scale + offset_y);
turtle.circle(radius * scale);
for (var r = radius * scale - circle_fill; r > 0 && circle_fill < 1; r -= circle_fill) {
turtle.jump(this.x * scale, this.y * scale - r + offset_y);
turtle.circle(r)
}
} else if (style == 1) {
const x = this.px * scale, y = this.py * scale + offset_y;
if (getDistance(x, y, turtle.x(), turtle.y()) > 0.1) {
turtle.jump(x, y);
}
turtle.goto(this.x * scale, this.y * scale + offset_y);
} else {
particles_to_draw.push(this.dup());
}
}
update() {
var x = this.x, y = this.y, px = this.px, py = this.py;
this.px = this.x; this.py = this.y;
// Verlet
const friction = 0.999;
x += (x - px) * friction;
y += (y - py) * friction;
y += gravity / 100 * Math.pow(this.current_life / max_life_t, 5);
const l = getDistance(x, y);
const rx = rotX(x/l, y/l, Math.PI / 2);
const ry = rotY(x/l, y/l, Math.PI / 2);
x += rx * l * max_variation * (this.rng_move.nextFloat() - 0.5);
y += ry * l * max_variation * (this.rng_move.nextFloat() - 0.5);
var dx = x - this.x;
var dy = y - this.y;
const l2 = getDistance(dx, dy);
const max_distance = 0.03;
if (l2 > max_distance) {
dx = dx / l2 * max_distance;
dy = dy / l2 * max_distance;
}
this.x += dx; this.y += dy;
const min_distance = 0.0001;
//if (l2 < min_distance) this.current_life = max_life_t;
//this.radius *= 0.993;
if (this.radius < 0.0001) this.current_life = max_life_t;
this.current_life++;
const spawn_mod = Math.max(20, Math.floor(this.spawn * (1 - this.current_life / 300)));
if ((this.current_life % spawn_mod) == 0) {
const x = this.x;
const y = this.y;
const angle = 1 * (this.rng_spawn.nextFloat() - 0.5);
const px = x - rotX(this.x - this.px, this.y - this.py, angle);
const py = y - rotY(this.x - this.px, this.y - this.py, angle);
const radius = this.radius; // * 0.9;
const current_life = Math.round(this.current_life / (this.rng_spawn.nextFloat() * 0.2 + 0.8));
const spawn = this.spawn; //Math.floor(this.spawn * 0.5);
return new Particle(x, y, px, py, radius, current_life, spawn);
}
return null;
}
isAlive() { return this.current_life < max_life_t; }
}
function rotX(x, y, a) { return Math.cos(a) * x - Math.sin(a) * y; }
function rotY(x, y, a) { return Math.sin(a) * x + Math.cos(a) * y; }
function getDistance(x1, y1, x2, y2) {
if (x2 === undefined) x2 = 0;
if (y2 === undefined) y2 = 0;
const dx = x1 - x2, dy = y1 - y2;
return Math.sqrt(dx*dx + dy*dy);
}
function initParticles() {
polygons = new Polygons();
const x = 0;
const y = 0;
const px = x + 0;
const py = y + 1;
const radius = thickness;
const current_life = 0;
const spawn = Math.floor(1000/spawn_rate);
new_particles = [];
new_particles.push(new Particle(x, y, px, py, radius, current_life, spawn));
particles_to_draw = [];
}
function walk(i, t) {
if (i==0) {
//max_life_t = max_life * (Math.cos(t * Math.PI * 2) + 1) / 2;
max_life_t = max_life * t;
initParticles();
}
var current_particle = null;
while (true) {
var early_exit = (i > max_iterations);
if (current_particle === null || early_exit) {
if (new_particles.length == 0 || early_exit) {
console.log(`Final iteration count: ${i-1}`);
return false;
}
current_particle = new_particles.shift();
}
const new_particle = current_particle.update();
if (new_particle != null) new_particles.push(new_particle);
if (current_particle.isAlive()) {
current_particle.draw();
} else {
if (particles_to_draw.length > 0) {
const points = [];
particles_to_draw.forEach( p => {
const l = getDistance(p.x, p.y, p.px, p.py);
const dx = rotX(p.x - p.px, p.y - p.py, Math.PI / 2) / l;
const dy = rotY(p.x - p.px, p.y - p.py, Math.PI / 2) / l;
const radius = p.getDrawRadius();
var p1x = (p.x + radius * dx) * scale ;
var p1y = (p.y + radius * dy) * scale + offset_y;
var p2x = (p.x - radius * dx) * scale;
var p2y = (p.y - radius * dy) * scale + offset_y;
points.push([p1x, p1y]);
points.unshift([p2x, p2y]);
});
if (style == 2) {
turtle.jump(points[0]);
points.forEach(p=>turtle.goto(p));
} else {
const p1 = polygons.create();
p1.addPoints(...points);
if (draw_hatching) p1.addHatching(-Math.PI/4, 1);
p1.addOutline();
polygons.draw(turtle, p1, true);
}
particles_to_draw = [];
}
break;
}
}
//sleep(100);
return true;
}
////
function sleep(milliseconds) {
const date = Date.now();
let currentDate = null;
do {
currentDate = Date.now();
} while (currentDate - date < milliseconds);
}
//// Random with seed
function RNG(_seed) {
// LCG using GCC's constants
this.m = 0x80000000; // 2**31;
this.a = 1103515245;
this.c = 12345;
this.state = _seed ? _seed : Math.floor(Math.random() * (this.m - 1));
}
RNG.prototype.nextFloat = function() {
// returns in range [0,1]
this.state = (this.a * this.state + this.c) % this.m;
return this.state / (this.m - 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
}
addPoints(...points) {
// 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];
}
addSegments(...points) {
// add segments (each a pair of points)
points.forEach(p => this.dp.push(p));
}
addOutline() {
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]);
}
}
addHatching(a, d) {
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);
if (addToVisList) polygonList.push(p);
}
};
}