Robert P. Munafo, 2002 Apr 16.
A smaller neighbor of a mu-atom is a neighbor that is smaller (has higher period). There are aleph-0 smaller neighbors in each direction (clockwise and counterclockwise). (By contrast, there are only two larger neighbors in each direction).
Example: R2.2/5a is a mu-atom. In the clockwise direction its smaller neighbors are R2.3/8a, R2.4/11a, R2.5/14a, R2.6/17a, etc. In the counterclockwise direction its smaller neighbors are R2.3/7a, R2.4/9a, R2.5/11a, R2.6/13a, etc. A few of these are seen in the figure below.
various mu-atoms, some of which are neighbors
Near the center of the figure is R2.3/8a. To the left (the counterclockwise direction) we see two of its neighbors, R2.2/5a and R2.5/13a. The smaller one of these, R2.5/13a, is a "smaller neighbor" of R2.3/8a because it is a neighbor and it is smaller.
revisions: 19980107 oldest on record; 20120416 add illustration
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11