How Are Images Created?
A computer program visualizes the set by giving each point a color depending
on whether or not that point is bounded or goes to infinity. If the point
remains bounded, then it is assigned the color black. Points that approach
infinity after n iterations can either be assigned the same color or, more
popularly, can be given a color based on how quickly they become unbounded
(Dewdney, 1989).
Since these images are created on a computer, it is important to remember
that only a small collection of points (approximately a few thousand to a
few million, depending on the power of your computer) are plotted for a
finite number of iterations. Therefore, a computer monitor can only
approximate the infinite number of points for an infinite number of
iterations.
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Copyright 1993, University of Illinois Board of Trustees
National Center for Supercomputing Applications, Education Group
rpanoff@ncsa.uiuc.edu and jgasaway@ncsa.uiuc.edu