# R2

Robert P. Munafo, 2008 Feb 2.

R2 is the R2-name for the entire Mandelbrot Set. This entry identifies its largest features; most of these have entries of their own.

The internal angle article gives precise formulas cor computing the coordinates of many of the features listed here.

## Major Features

In the ASCII ilustration on the right, features are identified with numbers 1 through 9. Explanations follow:
| vL , '"m-` -m/""\a, ... _,/Y, 3 ),., ., 5a 'YF-.F~"^' `'"~*eae/; 4 . \ -__/" '`_* 9 | )_. :c,_ \ ./- T\a | | ^F"-~~*a, /` dL | \_,\F^ '\` ."` _____\____._/"^" 2 1 .m~ ---7 ` ' :"r(, . ~e \__ __/ ` -\r._____/`L @e 8 _-""^)~*' ]c .^_ -~ ` / .)L_, _-`' / .]F_.,, ,.-e_@, 5b -*Y^ "~"v- -/-~* '`]- d@, 6 (, ^'"m-' :"^^` '^` |

Numbered features in the right-hand picture:

1 The solid cardioid-shaped region.

Colloquial: body, main cardioid, fixed-point cardioid

Technical: continent seed, the primary continental mu-atom

R2-Name: R2a

2 The largest solid circle.

Colloquial: head, 2-ball, west radical

Technical: mu-atom of period 2

R2-Name: R2.1/2a

3 (located straight up from 1) The second-largest solid circle (in a tie with #6)

Colloquial: 3-ball, north radical

Technical: a mu-atom of period 3

R2-Name: R2.1/3a

4 (line points down at feature) The largest island mu-molecule

Colloquial: period-3 minibrot, largest bug

Technical: second-largest mu-molecule, period-3 mu-molecule

R2-Name: R2F(1/2B1)S

5a (line points down into feature) The narrow region between Ra and R.1/2a .

Colloquial: seahorse valley (northern), fjord at -3/4+0i

R2-Name: R2.C(1/2)-

5b Colloquial: seahorse valley (southern)

R2-Name: R2.C(1/2)+

6 (located straight down from 1) The second-largest solid circle (in a tie with #3)

Colloquial: 3-ball, south radical

Technical: a mu-atom of period 3

R2-Name: R2.2/3a

7 (line points left towards feature) The cusp of the main cardioid.

Colloquial: elephant valley, east valley, fjord at 1/4+0i

R2-Name: R2.C(0)

8 ("bracket" indicating entire filament area) The entire filament "west" of R.1/2a .

Colloquial: main antenna, proboscis, spike

R2-Name: R2F(1/2B)

(contains the R2t Series)

9 The leftmost tip, the point -2+0i.

Colloquial: utter west

R2-Name: R2t or R2F(1/2B1)t

(limit of the R2t Series)

Here are some more details near the upper half of R2a :

| -./ 14--- -;c . ''Te.a\`` ---15 ._.(%_ .,,\ d^[^YF- ,_ ^`\-"`` ^`b(F- -*d` 11 '"m _,._:, .,. _,'"c, .*, _ ... -_ 'L))%_m,.-Y*e(""-^'` ''^-'-^e/*F- _., "F_, `_$ \/`^ `(e:-^"-r*%` _ .'^e- '" ]$- vmY/e"^ \ / `(^. _^Y/' \ / ^d__.:, $-` 12 13 "^"e@- "` 10 -^` ` '-a) 'F^ _[' |

Numbered features in the right-hand picture:

10 R2-Name: R2a (same as #1 above)

11 R2-Name: R2.1/3a (same as #3 above)

12 R2-Name: R2.2/5a

Colloquial: northwest radical.

13 R2-Name: R2.1/4a

Colloquial: northeast radical.

14 (line points to the right towards feature) The large minibrot above R.1/3a .

R2-Name: R2F(1/3B1)S

15 (Line points to the left towards feature) The point 0+i.

R2-Name: R2F(1/3B2){FS[2]FS[0]}x~

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 Jul 03. s.27