LogarithmicSpiralTest.as

package
{
	import flash.display.Graphics;
	import flash.display.Shape;
	import flash.display.Sprite;
	import flash.geom.Point;
	
	public class LogarithmicSpiralTest extends Sprite
	{
		public function LogarithmicSpiralTest()
		{
			var shape:Shape = new Shape();
			addChild(shape);
			shape.x = shape.y = 200;
			shape.graphics.lineStyle(0, 0xff0000, 1.0, true);
			plot(shape.graphics);
		}
		
		private function plot(canvas:Graphics):void
		{
			const eightPi:Number = Math.PI * 8;
			var interval:Number = Math.PI/20;	// this is the space between rays on the Wolfram page
			
			var steps:uint = 160;
			
			var point:Point;
			var lastPoint:Point = new Point(0, 0);
			
			canvas.moveTo(lastPoint.x, lastPoint.y);
			for (var theta:Number = interval; --steps > -1; theta += interval)
			{
				point = Point.polar(r(theta), theta);
				// flip y for Flash coordinate system:
				canvas.lineTo(point.x, -point.y);
				lastPoint = point;
			}
		}
	}
}

function r(theta:Number):Number
{
	const a:Number = 0.25;
	const b:Number = 0.25;
	return a * Math.exp(b * theta);
}

A comment on http://xtyler.com/code/104 asked how to implement the formula at http://mathworld.wolfram.com/LogarithmicSpiral.html