Neighbors

Robert P. Munafo, 2001 Jan 23.

Two mu-atoms are neighbors if they are siblings and they have no other siblings between them that are larger.

An equivalent definition is that the two mu-atoms are neighbors if the difference of their internal angles has a numerator of 1 (when expressed in reduced form). The internal angles are said to be adjacent fractions.

For example: R2.1/3a has the following neighbors: In the clockwise direction: R2.1/4a, R2.2/7a, R2.3/10a, R2.4/13a, R2.5/16a, (and so on); and in the counter-clockwise direction: R2.1/2a, R2.2/5a, R2.3/8a, R2.4/11a, R2.5/14a, (and so on).

See Farey addition.


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

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