ANALYSIS OF ABSTRACTION TO INFINITY


The standard Mandelbrot fractal equation takes the form z(n+1) = z(n)^2 + c, where c is the complex number x+iy corresponding to any point on the (x,y) coordinate plane. Fractal equations are iterative, in that the result of one calculation of the fractal equation becomes the z input to the next calculation. Over repeated evaluations of a fractal equation, values for each point in the (x,y) coordinate space either converge at single points, move toward the (0,0) origin point, or move toward infinity. The diverse colors in fractal plots reflect the rate of this movement for each point. Discussions of chaos theory frequently use fractals as examples, because slight variations in the fractal equation produce radically different results.

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