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If we examine points in the complex plane to see if
z^{2}+k diverges, where k is a fixed complex number, we
get the Julia set associated with the point k. Instead of
changing the constant in the function as we move from pixel to
pixel, we hold the value of k fixed as we scan the screen. Julia
sets and the Mandelbrot set are close relatives. The Julia set
boundary will be illuminated by the escape time algorithm as was
the case for the Mandelbrot set. Julia sets take several
different forms depending on the location in the plane of the
fixed point k.
