# Interior Distance Estimate

Robert P. Munafo, 1998 Apr 27.

An algorithm for estimating the distance from a point inside a mu-atom to the nearest point on the boundary of the mu-atom.

See The Science of Fractal Images, Appendix D.

The algorithm depends on counting the number of iterates in the Limit Cycle, and this determination is imprecise, because roundoff error affects the detection of the cycle. When in error, the period found is an integer multiple of the actual period (see Period for a more complete explanation).

However, this doesn't actually affect the distance estimate because the estimate is effectively the Nth root of a product of N terms, where N is the period, and when the period is in error the extra terms are just repeats of the limit cycle. So the Ns cancel out.

See also Distance Estimate, Interior Dwell

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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