Project-07-Butterfly Curve

// Sarah Luongo   
// sluongo
// sluongo@andrew.cmu.edu
// Project

/* This code aims to create the curve, butterfly curve, as explained on Wolfram
MathWorld. In addition to drawing the curve I played around with the fill color
and stroke depending on the X position of the mouse. */

// Setups canvas size and speed
function setup() {
    createCanvas(480, 480);
    frameRate(10);
}

// Draws the butterfly curve
function draw() {
    var red = random(255); // Random shade of red
    var green = random(255); // Random shade of green
    var blue = random(255); // Random shade of blue

    background(0); // Black background
    translate(width/2, height/1.64); // Translate to the "center" of canvas
    rotate(PI); // Rotate 180 degrees

    if (mouseX < width/3) {                           
        fill(red, green, blue); // Random fill color      
	stroke(0); // Black
	// Draws butterfly curve 4 times
        for (var i = 0; i < 4; i++) {
            drawButterflyCurve(i);
        }  
    } else if (mouseX >= width/3 & mouseX < 2*(width/3)) {
	noFill();
	stroke(red, green, blue); // Random stroke color
	// Draws butterfly curve 4 times
        for(var i = 0; i < 4; i++) {
            drawButterflyCurve(i*2); // i*2 makes size of curve bigger
        }
    } else if (mouseIsPressed) {
	background(225, 200, 255); // Purple background
	noFill();
	stroke(0); // Black
	drawButterflyCurve(1); // To see original curve
    } else {
	noStroke();
	fill(red, green, blue); // Random fill color
	// Draws butterfly curve 4 times
        for(var i = 0; i < 4; i++) {  
            drawButterflyCurve(i/3); // i/3 makes size of curve smaller
        }
    }
}

// Butterfly Curve
// https://mathworld.wolfram.com/ButterflyCurve.html
function drawButterflyCurve(j) {
    var da = .01; // How round the "wings" are
    var a = map(mouseX, 0, width, 0, width/9); // Constrain x size of butterfly curve 
    var b = map(mouseY, 0, height, 0, width/8); // Constrain y size of butterfly curve
    // Creates the butterfly curve
    beginShape();
    for (var t = 0; t <= 24*PI; t += da) {
	// The parametric equations found on the website commented above
	var r =  exp(cos(t))-2*cos(4*t)-pow(sin(t/12), 5);
	var x = a * sin(t) * r * j;
	var y = b * cos(t) * r * j;
	vertex(x, y);
    }
    endShape();
}