Fermat’s Spiral

x = stage.stageWidth / 2;
y = stage.stageHeight / 2;

var xp:Number = 0, yp:Number = 0;
var r:Number = 0, t:Number = 0;
var speed:Number = .07;
var scale:Number = 20;

var plot0:Shape = Shape(addChild(new Shape()));
var plot1:Shape = Shape(addChild(new Shape()));
plot0.graphics.lineStyle(0,0x000000);
plot1.graphics.lineStyle(0,0x000000);

addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
	 r =  scale * Math.sqrt(t);
	 xp =  r * Math.cos(t);
	 yp =  r * Math.sin(t);
	 t += speed;
	 
	plot0.graphics.lineTo(xp, yp);
    plot1.graphics.lineTo(-xp, -yp);
}

This snippet draws Fermat’s Spiral.