| Exploring the Mandelbrot Set |
Robert P. Munafo, 2002 Apr 18.
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.
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)
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