Analytical Naming System
Robert P. Munafo, 2002 Apr 27.
An Analytical Naming System is a system for assigning names based on precise analysis. Usually, a precise set of rules describes the way names are generated. For serious study of the Mandelbrot Set this is highly preferable to coordinates alone, or the use of colloquial names.
Why use an analytical naming system?
The R2 System (and the other systems listed below) are created because of a need (or desire) to organize the features of the Mandelbrot Set in a manner that is based on precise analytical techniques. The alternatives are not precise, and do not lend an understanding of the visual structure, the symmetries, etc.
Analytical systems used for the Mandelbrot Set
For the Mandelbrot Set, the following Analytical Naming Systems exist:
External angles, expressed as binary numbers or rational fractions, can be used as names. For human use, they are not very practical because no image or structure information is conveyed by the name. However, a computer can easily take an external angle and locate the corresponding feature.
The internal address is a more complete system than internal angle and can assign a name to every mu-unit owner. It uses internal angles and when necessary specifies mu-molecule seeds in the outward filament structure of a mu-unit by giving the period of the island. This naming system is used by Johannes Riedl
Internal angles, expressed as rational fractions, are used to name the secondary continental mu-atoms. They are quite useful and descriptive, and constitute the most concise simple system for naming mu-atoms within a set of children. Internal angles are used in several other analytical naming systems (including the R2 System) whenever a child must be specified.
Radical Names, AGDP
These names are equivalent to a subset of the R2 System. They focus on a small part of the Mandelbrot Set's complex patterns. They are quite useful and descriptive, and fairly easy to use.
The R2 Naming System
The R2 System is the most complex. It is based on a partial understanding of the patterns in the structures of the filaments. R2 can name everything that can be named by any of the other systems, and quite a bit more as well. For a complete description of the R2 system see the entry R2 Rules.
The Hubbard Tree is a graph (perhaps labeled and/or directed, there are different variations) whose structure is related to the dynamics of a Julia Set. There is a Hubbard Tree for each mu-atom and for each Misiurewicz point. It is possible to form a name from a Hubbard Tree by walking the nodes in a standard manner and listing their labels and other information in walk order.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2010 Sep 11. s.27