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 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 (see also the largest islands entry):
| Rank | R2-Name | period | Area of Island | Coordinates |
| 1 | R2F(1/2B1)S | 3 | 5.1012(39)e-4 | -1.759672 + 0i @ 0.067687 |
| 2 | R2F(1/3B1)S | 4 | 1.03356(67)e-4 | -0.158428 + 1.033350i @ 0.030476 |
| 4 | R2F(1/4B1)S | 5 | 3.4239(30)e-5 | 0.358431 + 0.643507i @ 0.017557 |
| 7 | R2F(1/5B1)S | 6 | 1.3693(13)e-5 | 0.442990 + 0.373727i @ 0.011104 |
| 14 | R2F(1/6B1)S | 7 | 6.1122(38)e-6 | 0.432259 + 0.227315i @ 0.007423 |
| 19 | R2F(1/7B1)S | 8 | 2.9529(17)e-6 | 0.404879 + 0.146216i @ 0.005150 |
| 36 | R2F(1/8B1)S | 9 | 1.5225(11)e-6 | 0.378631 + 0.098841i @ 0.003704 |
| 57 | R2F(1/9B1)S | 10 | 8.2995(45)e-7 | 0.356854 + 0.069659i @ 0.002734 |
| 87 | R2F(1/10B1)S | 11 | 4.7441(25)e-7 | 0.339454 + 0.050823i @ 0.002070 |
| 121 | R2F(1/11B1)S | 12 | 2.8278(16)e-7 | 0.325631 + 0.038164i @ 0.001596 |
| 182 | R2F(1/12B1)S | 13 | 1.74936(87)e-7 | 0.314596 + 0.029364i @ 0.001255 |
| 245 | R2F(1/13B1)S | 14 | 1.11702(73)e-7 | 0.305710 + 0.023064i @ 0.001003 |
| 329 | R2F(1/14B1)S | 15 | 7.3412(36)e-8 | 0.2984772 + 0.0184391i @ 0.0008128 |
| 445 | R2F(1/15B1)S | 16 | 4.9512(18)e-8 | 0.2925294 + 0.0149698i @ 0.0006675 |
| 577 | R2F(1/16B1)S | 17 | 3.4146(12)e-8 | 0.2875887 + 0.0123175i @ 0.0005544 |
| 733 | R2F(1/17B1)S | 18 | 2.40448(94)e-8 | 0.2834454 + 0.0102556i @ 0.0004652 |
| 930 | R2F(1/18B1)S | 19 | 1.72411(58)e-8 | 0.2799405 + 0.0086288i @ 0.0003939 |
| 1146 | R2F(1/19B1)S | 20 | 1.25736(47)e-8 | 0.2769515 + 0.0073283i @ 0.0003364 |
| 1434 | R2F(1/20B1)S | 21 | 9.3083(27)e-9 | 0.2743833 + 0.0062763i @ 0.0002894 |
| 1743 | R2F(1/21B1)S | 22 | 6.9893(23)e-9 | 0.2721616 + 0.0054163i @ 0.0002508 |
| 2104? | R2F(1/22B1)S | 23 | 5.3126(15)e-9 | 0.2702274 + 0.0047064i @ 0.0002187 |
| 2530? | R2F(1/23B1)S | 24 | 4.0873(12)e-9 | 0.2685336 + 0.0041153i @ 0.0001918 |
| 2999? | R2F(1/24B1)S | 25 | 3.1772(11)e-9 | 0.2670424 + 0.0036191i @ 0.0001691 |
| 3526? | R2F(1/25B1)S | 26 | 2.49460(85)e-9 | 0.2657229 + 0.0031995i @ 0.0001498 |
| 4063? | R2F(1/26B1)S | 27 | 1.97638(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) 1987-2024.
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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Feb 23.
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