Main Sequence  

Robert P. Munafo, 2009 Nov 5.



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 .

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 (see also the largest islands entry):

Rank R2-Name period Area of Island Coordinates
1 R2F(1/2B1)S 35.1012(39)e-4 -1.759672 + 0i @ 0.067687
2 R2F(1/3B1)S 41.03356(67)e-4-0.158428 + 1.033350i @ 0.030476
4 R2F(1/4B1)S 53.4239(30)e-5 0.358431 + 0.643507i @ 0.017557
7 R2F(1/5B1)S 61.3693(13)e-5 0.442990 + 0.373727i @ 0.011104
14 R2F(1/6B1)S 76.1122(38)e-6 0.432259 + 0.227315i @ 0.007423
19 R2F(1/7B1)S 82.9529(17)e-6 0.404879 + 0.146216i @ 0.005150
36 R2F(1/8B1)S 91.5225(11)e-6 0.378631 + 0.098841i @ 0.003704
57 R2F(1/9B1)S 108.2995(45)e-7 0.356854 + 0.069659i @ 0.002734
87 R2F(1/10B1)S 114.7441(25)e-7 0.339454 + 0.050823i @ 0.002070
121 R2F(1/11B1)S 122.8278(16)e-7 0.325631 + 0.038164i @ 0.001596
182 R2F(1/12B1)S 131.74936(87)e-7 0.314596 + 0.029364i @ 0.001255
245 R2F(1/13B1)S 141.11702(73)e-7 0.305710 + 0.023064i @ 0.001003
329 R2F(1/14B1)S 157.3412(36)e-8 0.2984772 + 0.0184391i @ 0.0008128
445 R2F(1/15B1)S 164.9512(18)e-8 0.2925294 + 0.0149698i @ 0.0006675
577 R2F(1/16B1)S 173.4146(12)e-8 0.2875887 + 0.0123175i @ 0.0005544
733 R2F(1/17B1)S 182.40448(94)e-8 0.2834454 + 0.0102556i @ 0.0004652
930 R2F(1/18B1)S 191.72411(58)e-8 0.2799405 + 0.0086288i @ 0.0003939
1146 R2F(1/19B1)S 201.25736(47)e-8 0.2769515 + 0.0073283i @ 0.0003364
1434 R2F(1/20B1)S 219.3083(27)e-9 0.2743833 + 0.0062763i @ 0.0002894
1743 R2F(1/21B1)S 226.9893(23)e-9 0.2721616 + 0.0054163i @ 0.0002508
2104?R2F(1/22B1)S 235.3126(15)e-9 0.2702274 + 0.0047064i @ 0.0002187
2530?R2F(1/23B1)S 244.0873(12)e-9 0.2685336 + 0.0041153i @ 0.0001918
2999?R2F(1/24B1)S 253.1772(11)e-9 0.2670424 + 0.0036191i @ 0.0001691
3526?R2F(1/25B1)S 262.49460(85)e-9 0.2657229 + 0.0031995i @ 0.0001498
4063?R2F(1/26B1)S 271.97638(59)e-9 0.2645500 + 0.0028424i @ 0.0001334
? R2F(1/100B1)S 101 ≅ 5e-13 0.25098947 + 0.00004931i @ 0.0000007


revisions: 20031218 oldest on record; 20091105 add all rows above rank 182 period 13




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


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