Project 07: Butterfly Curve

var n = 100; //Number of points
var r = 50; //Radius

var x = [] //List of X values
var y = [] //List of Y values
var t = [] //Parameter 


function setup() 
{
	createCanvas(480, 480);
	frameRate(60)
	//Initialize Butterfly curve by assigning X, Y and T values
    for (let i = 0; i < n; i++) {
        t[i] = random(0, 180);
        //Equations taken from https://mathworld.wolfram.com/ButterflyCurve.html
        x[i] = r * sin(t[i]) * (exp(cos(t[i])) - 3 * cos(4 * t[i]) - pow(sin(t[i] / 10), 5));
        y[i] = r * cos(t[i]) * (exp(cos(t[i])) - 3 * cos(4 * t[i]) - pow(sin(t[i] / 10), 5));
    }
}


function draw() 
{

    background(0);
    //Make (0,0) center of canvas
    translate(width / 2, height / 2);


    let my = map(mouseY,0,height,18*PI,6*PI); //Map mouse Y to number of rotation iterations of butterflies
    push();
   	noFill();
    stroke(100)
    strokeWeight(0.25)

    //Begin curve for butterfly
    beginShape();
    for (let i = 0; i < my; i += 0.01)
    {
    	//Equations taken from https://mathworld.wolfram.com/ButterflyCurve.html
      	let bx = r * sin(i) * (exp(cos(i)) - 3 * cos(4 * i) - pow(sin(i / 10), 5));
      	let by = r * cos(i) * (exp(cos(i)) - 3 * cos(4 * i) - pow(sin(i / 10), 5));
      	//Vertex has X and Y points corresponding to parametric equations
      	vertex(bx,by)
    }
    endShape();
    pop();

    //Draw flying circles
    push();
    fill(255);
    noStroke();
    //Loop for number of circles
    for (let i = 0; i < n; i++) 
    {
    	let mx = map(mouseX,0,width,-0.005,0.005); //Map mouse X to speed at which parameter changes (from negative to positive speeds)
        t[i] += mx; //Add mapped mouse X to parameter

        //Reset parameter if it exceeds 180 degrees
        if (t[i] > 180)
        {
        	t[i] = 0;
        }

        //Equations taken from https://mathworld.wolfram.com/ButterflyCurve.html
        x[i] = r * sin(t[i]) * (exp(cos(t[i])) - 3 * cos(4 * t[i]) - pow(sin(t[i] / 10), 5));
        y[i] = r * cos(t[i]) * (exp(cos(t[i])) - 3 * cos(4 * t[i]) - pow(sin(t[i] / 10), 5));

        //Draw circle
        circle(x[i], y[i], 3);
    }
    pop();
}