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 Angle
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.
Internal Address
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 Angle
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.
Hubbard trees
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) 1987-2024.
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