Largest
Robert P. Munafo, 2023 Mar 22.
The term "larger" is sometimes used in this encyclopedia to refer to a relationship between muatoms that are siblings: A muatom is "larger" if it has a lower period. The word is used in this way on the pages: binary search for internal angle, internal angle, larger neighbor, neighbors, and secondary continental muatom. The "larger neighbor" term is also used elsewhere, e.g. Farey addition. See also smaller.
R2.1/3a is "larger" than R2.2/5a because it has a lower period
For more examples of larger neighbors, see the table in the secondary continental muatom article.
Being "larger" in this sense does not necessarily mean that a muatom is physically larger: for example, R2.3/8a is physically larger than R2.1/7a, but is smaller in the sense meant here, because it has a higher period.

In the images above, both muunits are shown at the same scale (image width and height are 0.1 units on the real and imaginary axis respectively). But the muatom with the lower period is also physically smaller. This is a counterexample to the ordinary rule that siblings with a lower period are physically larger. The discrepancy is accounted for by the sin(2π N/M) term in the "Milnor's approximation" formula shown in the secondary continental muatom article.
Some Things That Are "Largest"
The largest muatom is the entire Mandelbrot set itself, but commonly the term is used to refer to the largest secondary continental muatom, which is R2.1/2a. Likewise, the largest muunit (aside from the entire Mandelbrot set treated as a muunit) is R2.1/2.
The largest mumolecule is also the entire Mandelbrot set, and the largest island mumolecule is R2F(1/2B1)S.
revisions: 20120416 oldest on record; 20230322 add "some things..." section
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 19872024.
Muency main page — index — recent changes — DEMZ
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Mar 24. s.27