Robert P. Munafo, 1999 Feb 2.
The commonly-seen views of the Mandelbrot Set have been challenged by
arguments based on techniques like error-term analysis. They show that
if you want to get an accurate view of a lemniscate ZN you need
to use at least N digits in all your calculations. The result is
that most views of the Mandelbrot Set that people see on computers are
(in theory) completely inaccurate.
However, an overwhelming amount of experimental evidence shows that
the views are indistinguishable by the human eye regardless of how
many digits you use, as long as the number of digits is sufficient to
distinguish the coordinates of the parameter value C.
See also aliasing errors, computability, iteration algorithm,
magnification, precision, resolution.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index
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