Main Sequence

Robert P. Munafo, 2003 Dec 18.

The Main Sequence is the set of secondary continental mu-atoms with internal angle 1/N for integer N>2, and R2 names R2.1/Na; the first few are R2.1/2a, R2.1/3a, R2.1/4a, etc. See also the entries for R2 and R2C(0).

The orbital dynamics of the main sequence mu-atom R2.1/Na is the simplest of all period-N mu-atoms.

The main sequence mu-atoms decrease in size in a manner that is proportional to the cube of the period: the main-sequence mu-atom of period 2N will be 1/8 the size of the main-sequence mu-atom of period N. See secondary continental mu-atoms for the formula from which this is derived.

Each has a largest island, R2F(1/NB1)S. Like the mu-atoms, their size goes down in proportion to the cube of the period. The period of R2F(1/NB1)S is always N+1. The area of the island of period P+1 is approximated by the formula

Ap+1 ≅ 0.05 sin2(π/p) / p4

Here is a table of the largest, extracted from the largest islands entry:


Rank R2-Name period Area of Island Coordinates
1 R2F(1/2B1)S 3 5.1023e-04 -1.759672 + 0i @ 0.067687
2 R2F(1/3B1)S 4 1.0334e-04 -0.158428 + 1.033350i @ 0.030476
4 R2F(1/4B1)S 5 3.4253e-05 0.358431 + 0.643507i @ 0.017557
7 R2F(1/5B1)S 6 1.3700e-05 0.442990 + 0.373727i @ 0.011104
14 R2F(1/6B1)S 7 6.1069e-06 0.432259 + 0.227315i @ 0.007423
19 R2F(1/7B1)S 8 2.9532e-06 0.404879 + 0.146216i @ 0.005150
36 R2F(1/8B1)S 9 1.5221e-06 0.378631 + 0.098841i @ 0.003704
57 R2F(1/9B1)S 10 8.3044e-07 0.356854 + 0.069659i @ 0.002734
87 R2F(1/10B1)S 11 4.7450e-07 0.339454 + 0.050823i @ 0.002070
121 R2F(1/11B1)S 12 2.8280e-07 0.325631 + 0.038164i @ 0.001596
2530 R2F(1/23B1)S 24 4.0861e-09 0.268534 + 0.004115i @ 0.000192
? R2F(1/100B1)S 101 ≅ 5e-13 0.25098947 + 0.00004931i @ 0.0000007


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

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