# Parameter

Robert P. Munafo, 2002 May 6.

The value (always a complex number) that gets added at each step of the quadratic iteration that produces a Julia set. This number is usually called C. For each distinct valus of C there is a distinct Julia set with a unique shape.

In more general usage, a value that gets used in the iteration formula
for some type of iteration whose dynamics is being studied. The
iteration itself happens in the "dynamical plane", and the set of all
possible parameters is the "parameter plane". In most types of
iteration functions it has been found that there are areas of the
parameter plane (i.e. certain parameter values) for which the
iteration exhibits the same properties as the simple quadratic
function Z'=Z^{2}+C, and those regions of the parameter plane contain
shapes that look like the Mandelbrot set.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.

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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2002 May 07. s.27