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Larger Neighbor    

Robert P. Munafo, 2012 Apr 16.

A "larger neighbor" of a mu-atom is another mu-atom that is larger (has lower period). There are at most two; one in the clockwise direction and one counterclockwise. (By contrast, there are aleph-0 smaller neighbors in each direction).

If A and B are the larger neighbors of C, then C is the inner neighbor is A and B.

Example: R2.2/5a is a mu-atom. Its two larger neighbors are R2.1/2a and R2.1/3a.

More examples:

various mu-atoms, some of which are neighbors
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 larger one of these, R2.2/5a, is a "larger neighbor" of R2.3/8a because it is a neighbor and it is larger.

Similarly, to the right (the clockwise direction) of R2.3/8a we find R2.4/11a and R2.1/3a. The first of these is a smaller neighbor and the other is a larger neighbor.

See also inner neighbor, internal angle, smaller neighbor, Farey addition.

revisions: 20010123 oldest on record; 20120416 add illustration

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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