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[SWF(width = 600, height = 600)]
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var a:Number = 0.02;
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var b:Number = .9998;
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var xn1:Number = 5;
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var yn1:Number = 0;
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var xn:Number, yn:Number;
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var scale:Number = 10;
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var iterations:Number = 20000;
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function f(x:Number):Number{
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var x2:Number = x * x;
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return a * x + (2 * (1 - a) * x2) / (1 + x2);
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}
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var canvas:BitmapData = Bitmap(addChild(new Bitmap(new BitmapData(600,600,false,0xEFEFEF)))).bitmapData;
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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canvas.fillRect(canvas.rect, 0xEFEFEF);
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a = mouseY / 1000;
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xn1 = mouseX / 30;
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yn1 = 0;
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for (var i:int = 0; i<iterations; i++){
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xn = xn1;
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yn = yn1;
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xn1 = b * yn + f(xn);
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yn1 = -xn + f(xn1);
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canvas.setPixel( 280 + xn1 * scale, 300 + yn1 * scale, 0x000000);
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}
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}
Notice the setup for this is very similar to yesterdays flames attractor post.
Back in october of last year I stumbled upon the excellent subblue website by Tom Beddard. I was REALLY impressed by a blog post about Gumowski / Mira patterns. If you haven't seen it you should go take a look.
I'd never heard of Gumowski / Mira patterns before and made a mental note to go and try to read about them and maybe find an equation to port to actionscript or processing. Anyway, a few days ago I decided to go ahead and look up the math and... this is the result.
I got equation over at mathworld...
For simplicity I intentionally made the actionscript code look as much like the mathworld equation as possible. Using f for my function name and using xn1, yn1 etc... There are a few speed optimizations that could be made but I wanted this snippet to be very readable.
Here are a few examples of what this code will generate:
