# Ridgeline

Robert P. Munafo, 2023 Mar 20.

This is a term used to refer to the filaments and/or the field lines by some students of the Mandelbrot set, including P. Michael Hutchins.

The name is derived from the common usage terms "ridge" and "ridgeline" that refer to terrain feature, as in this definition from the Wikipedia article:

A ridge is a long, narrow, elevated geomorphologic landform, structural feature, or combination of both separated from the surrounding terrain by steep sides. The sides of a ridge slope away from a narrow top, the crest or ridgecrest, with the terrain dropping down on either side. The crest, if narrow, is also called a ridgeline.

Since the Mandelbrot set is not a three-dimensional object, we need to do a little extra work to impose a 3-D interpretation upon it; see that article for details.

When continuous dwell is used, ridges can be computed in a practical way using gradient descent (with the height inverted, so that points of higher dwell have a lower altitude); then the ridgelines will be the same as the path taken by a particle with no mass or momentum that follows the steepest available downhill gradient. The particle can begin anywhere in the exterior of the Mandelbrot set and will take a path similar to a field line.

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

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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