Largest  

Robert P. Munafo, 2012 Apr 16.



The term "larger" is sometimes used in this encyclopedia to refer to a relationship between mu-atoms that are siblings: A mu-atom 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 mu-atom. 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
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 mu-atom article.

Being "larger" in this sense does not necessarily mean that a mu-atom 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.

R2F(1/7(*B))
R2F(1/7(*B))
R2F(3/8(*B))
R2F(3/8(*B))

In the images above, both mu-units are shown at the same scale (image width and height are 0.1 units on the real and imaginary axis respectively). But the mu-atom with the lower period is also physically smaller. This is a counter-example 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 mu-atom article.




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017.     Mu-ency index


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