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The Mandelbrot set is calculated for each point (x,y). The color is determined by how many times a certain set of calculations can be done before it goes out of a set range. The range in this case is within 2 of the origin (i.e.- if new_x^2 + new_y^2 >4, it's out of range). new_x is found by cur_x^2-cur_y^2+x, and new_y = 2*cur_x*cur_y+y. The first time the calculation is done, cur_x and cur_y are both zero. The second time, the previous new_x and new_y become the cur_x and cur_y in the second time through. You keep doing it until new_x^2+new_y^2>4. Of course, some points in the Mandelbrot set (represented in black) never get out of the range, no matter how many times you do it (for example, (0,0). The first time you do it, new_x=0^2-0^2+0, and new_y=2*0*0+0. The next time through, cur_x and cur_y would still both be 0, so it would continue at (0,0) forever). The set colors and so forth are the most basic, easy ones, feel free to play with them, and the coordinates I have set let you see basically the entire part that's worth seeing, but feel free to zoom out or zoom in at your whim. I made it so you can more easily zoom in by making it so you can click in a couple spots (which it logs as x1, y1 and x2, y2, in which x1, y1 will always be the upper left corner). Set your bounds like that, hit Set X/Y and then redraw to draw that smaller area. Hit Reset X/Y if you want to start over and make your new boundries over (just to make sure it does them right). The valid values for the initial red, green, and blue values are between 0 and 255. The incrementing values can be just about anything, but I'm not sure how well negative numbers work (they do, but I'm not sure if their bounds are as nice, I would normally just add a larger positive number, i.e.- 252 instead of -3, just to make sure). Use the zoom out button to zoom out to a level 3 times the dimensions of the current level. Also, feel free to see a more versitile applet that is capable of manipulating the Mandelbrot set and also a closely related fractal called the Julia Set. This page also has a more accurate explanation of the math involved.

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CS142

Fractals

These applets were developed by Matthew Reeder. Please get my permission before using these applets on your own site.

(And trust me, it will be easier if I help you use them :-p)