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cheap java website hosting cheap java website hosting Here and in the future we are going to try to separate the mathematical definition of our data from its display on the screen. In fact we won't even add the screen display till the second iteration of the program.Our data structure will be a two dimensional array, each element of which represents a fixed point in the complex plane. The array is defined by the value of the lower left point, the gap between points and the number of pixels in the x and y directions. Thus given that element (0,0) of the array matches the complex point (x0,y0), each point is separated by a value gap, we know that element i,j of the array represents the point (x0 + i*gap, y0 + j*gap) in the complex plane.

cheap java website hosting Since we know this by position of the array element alone we dont' need to store this value in the array.What will we store in each element of this array? We'll calculate a number to go there in the following fashion. Let z = 0 + 0i and let c be the position of that array element in complex space. calculate z = z*z + c and iterate as follows up to 200 times:for (i=0; i < 200; i++) { z = z.Times(z) + c; }The Mandelbrot set is composed of those elements which, no matter how long we do this, never approach infinity.

cheap java website hosting Since infinity can take a mighty long time to approach, it's fortunate that a fairly elementary theorem in complex variable theory guarantees that any number whose magnitude ever exceeds two in this iterative scheme will become as large as one might wish. (i.e. They asymptotically approach infinity.) Therefore once a number exceeds two we can break out of the loop and say definitively that this number is not in the Mandelbrot set.

cheap java website hosting Unfortunately there's no guarantee that just because an element doesn't reach 2 in two hundred iterations it might not reach two on the two hundredth and first iteration or the two thousandth or the two millionth. However most numbers that don't prove they're not in the Mandelbrot Set by the two hundredth iteration are reasonably likely to be in it.Here's how the code will work. First we'll select the lower left hand corner of our rectangle in complex space, the size of the gap between the points and the number of points in each dimension. For a specific example we can choose the square bordered on the lower left by (-2,-2) and on the upper right by (2,2).

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