# Exploring the Mandelbrot Set

Robert P. Munafo, 2002 Apr 18.

Most people who encounter the Mandelbrot set and begin to explore it discover its various features in a particular order. Each is discussed separately. In order of discovery, these features are:

1. The Continent (and self-similarity).

2. The Filaments and dwell bands.

3. The Island mu-molecules.

4. Filament Symmetry including self-similarity and two types of rotational symmetry (related to mu-atom Periods and bifurcation).

and then, at roughly the same time:

5a. Nested Filament Symmetries

5b. The unique attributes of Cusp filaments

Then one reaches a bit of a lull. To most observers, these properties seem to account for everything in the structure of the Mandelbrot Set. In fact, most people will stop here, and some technically-minded enthusiasts have devised Naming Systems based on these features alone (plus possibly the External Arguments).

Persistent explorers and those with a more mathematical background will also discover:

- The External Arguments.

- The Embedded Julia Sets.

- The Second-Order Embedded Julia Sets.

See also:

algorithms, for discussion of how to write a Mandelbrot program.

history, for a brief history of the Mandelbrot Set's exploration.

R2 for a guide to the largest features of the Mandelbrot Set.

enumeration of features for a discussion of the various number sequences that are discovered when the Mandelbrot set's features are counted.

See also features, Feigenbaum point, paramecia, R2.C(1/2)

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2012. Mu-ency index