Adjacent Fractions
Robert P. Munafo, 2001 Jan 23.
Two fractions a/b and c/d are adjacent if there is an integer e such that a/b + 1/e = c/d or c/d + 1/e = a/b. In the Mandelbrot set, if two siblings are neighbors, their internal angles are adjacent fractions. For example, R2.1/3a and R2.2/5a are neighbors, and the difference of the internal angles is 1/15.
The converse is not true. For example, 2/5 minus 1/6 is 7/30, but R2.7/30a and R2.2/5a are not neighbors (R2.1/4a, R2.1/3a, and R2.4/17a lie between them).
See also between, Farey addition.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index
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