Inner Neighbor

Robert P. Munafo, 2001 Jan 23.


Given two mu-atoms that are neighbors, the inner neighbor (also called the common smaller neighbor) is the largest mu-atom between them. "Between" in this case refers to any mu-atoms that you encounter as you travel along the boundary of the parent from one sibling to the other. (There are two ways you can go, the way you should go is the way that doesn't cross the parent's parent or the parent's cusp if the parent is a seed.)

Examples: R2.1/2a and R2.1/3a are neighbors. Their inner neighbor is R2.2/5a.

See also larger neighbor, smaller neighbor, Farey addition.



From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index


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