/**
 * Julia interactive
 * By Raphael Rouvinov-Kats
 * 
 * Whipped this one out in a cool five minutes ;)
 * https://en.wikipedia.org/wiki/Julia_set#Quadratic_polynomials
 * */

frameRate(0);

var max_iters = 20;

// function prototypes
var complexFromPolar;

var Complex = function(a,b) {
    this.a = a;
    this.b = b;
    
    this.conj = function() {
        return new Complex(this.a, -this.b);
    };
    
    this.re = function() {
        return this.a;
    };
    
    this.im = function() {
        return this.b;
    };
    
    this.add = function(c2) {
        return new Complex(this.a+c2.a, this.b+c2.b);
    };
    
    this.sub = function(c2) {
        return new Complex(this.a-c2.a, this.b-c2.b);
    };
    
    this.prod = function(c2) {
        return new Complex(this.a * c2.a - this.b * c2.b, this.b*c2.a + this.a*c2.b);
    };
    
    this.div = function(c2) {
        return new Complex((this.a*c2.a+this.b*c2.b)/(c2.a*c2.a+c2.b*c2.b), (this.b*c2.a-this.a*c2.b)/(c2.a*c2.a+c2.b*c2.b));
    };
    
    this.inv = function() {
        return new Complex(this.a/(this.a*this.a+this.b*this.b), -this.b/(this.a*this.a+this.b*this.b));
    };
    
    this.r = function() {
        return sqrt(this.a*this.a+this.b*this.b);
    };
    
    this.r2 = function() {
        return this.a*this.a+this.b*this.b;
    };
    
    this.angleTo = function(c2) {
        return acos((this.a*c2.a+this.b*c2.b)/(this.r()*c2.r()));
    };
    
    this.phi = function() {
        return atan2(this.b, this.a);
    };
    
    // assuming p integer
    this.pow = function(p) {
        return new complexFromPolar(p*this.phi(), pow(this.r(),p));
    };
};

var complexFromPolar = function(t,r) {
    return new Complex(r*cos(t), r*sin(t));
};

var julia_of_point = function(x, y, c, d) {
    var a = map(x, 0, width, -2, 2);
    var b = map(y, 0, height, -2, 2);
    
    for (var i = 0; i < max_iters; i++) {
        // z**2+c == (a+bi)(a+bi)+(c+di) == (a*a-b*b+c) + i(2ab+d)
        // var new_a = a*a-b*b+c;
        // var new_b = 2*a*b+d;
        // if (sqrt(new_a*new_a + new_b*new_b) > 2) {
        //     return i;
        // }
        // a = new_a;
        // b = new_b;
        
        if (sqrt(a*a*a - b*b*b - b*d-a*c) > 0) {
            return i;
        }
    }
    
    return -1;
    
    // return -1;
};

var julia = function(posX, posY) {
    if (!this.loadPixels) { return; }
    this.loadPixels();
    var pix=this.imageData.data;
    
    var c = map(posX, 0, width, -2, 2);
    var d = map(posY, 0, height, -2, 2);
    
    var l = 401 * 401;
    while(l--) {
        var x = l % 401;
        var y = (l-x)/401;
        
        // var dx = posX - x;
        // var dy = posY - y;
        // var d = sqrt(dx*dx + dy*dy);
        // d = map(d, 0, sqrt(width*width+height*height), 0, 255);
        
        var v = julia_of_point(x, y, c, d);
        
        
        var ind = (x + y * 400) << 2;
        if (v === -1) {
            pix[ind]   = 0;
            pix[ind+1] = 0;
            pix[ind+2] = 0;
            continue;
        }
        
        v = map(v, 0, max_iters, 0, 255);
        pix[ind]   = 128 + v/2;
        pix[ind+1] = 192 + v/4;
        pix[ind+2] = v;
    }
    
    this.updatePixels();
};

var mouseDragged = function() {
    julia(mouseX, mouseY);
};

julia(100, 200);