# Absolute Value

Robert P. Munafo, 2023 Mar 20.

Definition : math. The distance from the origin of a point a + bi, given by the formula sqrt( a

^{2}+ b

^{2}).

The absolute value is also called the magnitude of a complex number, or sometimes it is called the "radius" in reference to the polar coordinate system.

Computing the magnitude is important for the escape radius test during iteration; but a optimization to avoid the square root is to compare to the square of the escape radius rather than taking a square root and comparing to the escape radius itself.

revisions: 19981207 oldest on record; 20120424 synonym "magnitude"; 20230320 escape radius optimization

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 2023 Mar 20. s.27