* Under Creative Commons License

 * https://creativecommons.org/licenses/by-sa/4.0/

 * Written by Juan Carlos Ponce Campuzano, 19-Jul-2018

 */

​

// Updated Jan-2019

​

let easycam;

let particles = [];

​

let points = [];

​

let attractor;

​

let NUM_POINTS = 3500;//num of points in curve

​

let numMax = 600;

let t = 0;

let h = 0.009;

let currentParticle = 0;

​

// settings and presets

let parDef = {

Attractor: 'Halvorsen',

Speed: 1.0,

Particles: true,

Preset: function() {

    removeElements();

    this.Speed = 1.0;

    this.Particles = true;

    attractor.a = 1.89;

    attractor.x = -1.48;

    attractor.y = -1.51;

    attractor.z = 2.04;

    for (let i=points.length-1; i>=0; i-=1){

        points.splice(i,1);

    }

    initSketch();

},

Randomize: randomCurve,

};

​

​

function backAttractors () {

    window.location.href = "https://jcponce.github.io/strange-attractors/#halvorsen";

}

​

​

function setup() {

    attractor = new HalvorsenAttractor();

    // create gui (dat.gui)

    let gui = new dat.GUI();

    gui.add(parDef, 'Attractor');

    gui.add(parDef, 'Speed', 0, 3, 0.01).listen();

    gui.add(parDef, 'Particles' );

    gui.add(parDef, 'Randomize'  );

    gui.add(parDef, 'Preset'  );

    gui.add(this, 'backAttractors').name("Go Back");

    pixelDensity(1);

    let canvas = createCanvas(windowWidth, windowHeight, WEBGL);

    setAttributes('antialias', true);

    console.log(Dw.EasyCam.INFO);

    easycam = new Dw.EasyCam(this._renderer, {distance : 40});

    // place initial samples

    initSketch();

}

​

function windowResized() {

    resizeCanvas(windowWidth, windowHeight);

    easycam.setViewport([0,0,windowWidth, windowHeight]);

}

​

function randomCurve() {

    removeElements();

    for (var i = points.length-1; i>=0; i-=1){

        points.splice(i,1);

    }

    attractor.randomize();

    initSketch();

}

​

function initSketch(){

    var hleft = select('#hud-left');

    var hright = select('#hud-right');

    createElement('li', 'a = '+ nfc(attractor.a,2) ).parent(hleft);

    createElement('li', '----------' ).parent(hleft);

    createElement('li', 'x<sub>0</sub> = '+ nfc(attractor.x,2) ).parent(hleft);

    createElement('li', 'y<sub>0</sub> = '+ nfc(attractor.y,2) ).parent(hleft);

    createElement('li', 'z<sub>0</sub> = '+ nfc(attractor.z,2) ).parent(hleft);

    let p = {

    x: attractor.x,

    y: attractor.y,

    z: attractor.z

    }

    for( var j = 0; j < NUM_POINTS; j++ ) {

        p = attractor.generatePoint( p.x, p.y, p.z );

        if( isNaN( p.x ) || isNaN( p.y ) || isNaN( p.z ) ) {

            console.log( 'Failed, retry' );

            randomCurve();

            return;

        }

        points.push(new p5.Vector(attractor.scale * p.x,attractor.scale * p.y, attractor.scale * p.z));

    }

    let m = 20;

    for (var i=0; i < numMax; i++) {

        particles[i] = new Particle(random(-m, m), random(-m, m), random(-m, m), t, h);

    }

}

​

​

function draw(){

    // projection

    perspective(60 * PI/180, width/height, 1, 5000);

    // BG

    background(0);

    translate(0,0,-5);

    rotateX(-0.5);

    rotateY(PI/2+0.7);

    beginShape(POINTS);

    for (let v of points) {

        stroke(234, 193, 255);

        strokeWeight(0.1);

        vertex(v.x, v.y, v.z);

    }

    endShape();

    if(parDef.Particles==true){

    //updating and displaying the particles

    for (let i=particles.length-1; i>=0; i-=1) {

        let p = particles[i];

        p.update();

        p.display();

        if ( p.x > 100 ||  p.y > 100 || p.z > 100 || p.x < -100 ||  p.y < -100 || p.z < -100 ) {

            particles.splice(i,1);

            currentParticle--;

            particles.push(new Particle(random(-5,5),random(-5,5),random(-5,5),t,h) );

        }

    }

    }

    // gizmo

    //strokeWeight(0.1);

    //stroke(255, 32,  0); line(0,0,0,2,0,0);

    //stroke( 32,255, 32); line(0,0,0,0,2,0);

    //stroke(  0, 32,255); line(0,0,0,0,0,2);

}

​

​

function componentFX(t, x, y, z){

    return 0.3 * parDef.Speed * ( -attractor.a * x -4 * y-4 * z-y * y );//Change this function

}

​

function componentFY(t, x, y, z){

    return 0.3 * parDef.Speed * (  -attractor.a * y-4 * z-4 * x-z * z   );//Change this function

}

​

function componentFZ(t, x, y, z){

    return 0.3 * parDef.Speed * ( -attractor.a * z-4 * x-4 * y-x * x);//Change this function

}

​

//Particle definition and motion

class Particle{

    constructor(_x, _y, _z, _t, _h){

        this.x = _x;

        this.y = _y;

        this.z = _z;

        this.time = _t;

        this.radius = 0.2;

        this.h = _h;

        this.r = random(255);

        this.g = random(200,255);

        this.b = random(200,255);

    }

    update() {

        this.k1 = componentFX(this.time, this.x, this.y, this.z);

        this.j1 = componentFY(this.time, this.x, this.y, this.z);

        this.i1 = componentFZ(this.time, this.x, this.y, this.z);

        this.k2 = componentFX(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k1, this.y + 1/2 * this.h * this.j1, this.z + 1/2 * this.h * this.i1);

        this.j2 = componentFY(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k1, this.y + 1/2 * this.h * this.j1, this.z + 1/2 * this.h * this.i1);

        this.i2 = componentFZ(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k1, this.y + 1/2 * this.h * this.j1, this.z + 1/2 * this.h * this.i1);

        this.k3 = componentFX(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k2, this.y + 1/2 * this.h * this.j2, this.z + 1/2 * this.h * this.i2);

        this.j3 = componentFY(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k2, this.y + 1/2 * this.h * this.j2, this.z + 1/2 * this.h * this.i2);

        this.i3 = componentFZ(this.time + 1/2 * this.h, this.x + 1/2 * this.h * this.k2, this.y + 1/2 * this.h * this.j2, this.z + 1/2 * this.h * this.i2);

        this.k4 = componentFX(this.time + this.h, this.x + this.h * this.k3, this.y + this.h * this.j3, this.z + this.h * this.i3);

        this.j4 = componentFY(this.time + this.h, this.x + this.h * this.k3, this.y + this.h * this.j3, this.z + this.h * this.i3);

        this.i4 = componentFZ(this.time + this.h, this.x + this.h * this.k3, this.y + this.h * this.j3, this.z + this.h * this.i3);

        this.x = this.x + this.h/6 *(this.k1 + 2 * this.k2 + 2 * this.k3 + this.k4);

        this.y = this.y + this.h/6 *(this.j1 + 2 * this.j2 + 2 * this.j3 + this.j4);

        this.z = this.z + this.h/6 *(this.i1 + 2 * this.i2 + 2 * this.i3 + this.i4);

        this.time += this.h;

    }

    display() {

        push();

        translate(this.x, this.y, this.z);

        ambientMaterial(this.r, this.b, this.g);

        noStroke();

        sphere(this.radius, 7, 6);

        pop();

    }

}

​

class HalvorsenAttractor {

    constructor(){

    this.speed = 0.5;

    this.a = 1.89;

    this.x = -1.48;

    this.y = -1.51;

    this.z = 2.04;

    this.h = 0.03;

    this.scale = 1;

    }

​

   generatePoint( x, y, z ) {

    var nx = this.speed * (-this.a * x -4 * y-4 * z-y * y ) ;

    var ny =  this.speed * ( -this.a * y-4 * z-4 * x-z * z  ) ;

    var nz =  this.speed * ( -this.a * z-4 * x-4 * y-x * x );

    x += this.h * nx; y += this.h * ny; z += this.h * nz;

    return { x: x, y: y, z: z }

}

​

    randomize() {

    this.a = random( 0.1,  3 );

    this.x = random( -5, 5 );

    this.y = random( -5, 5 );

    this.z = random( -5, 5 );

}

​

}