Actionscript:
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var xp:Number=Math.random() * stage.stageWidth;
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var yp:Number=Math.random() * stage.stageHeight;
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graphics.lineStyle(0,0x000000);
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graphics.moveTo(xp, yp);
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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xp+=Math.random()*10-5;
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yp+=Math.random()*10-5;
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graphics.lineTo(xp, yp);
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}
Nothing special here, but its good to know that this technique has a name... and that it's NOT Brownian Motion... more here.