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:


-0.759 +0.000i  +2.500
-0.759 +0.000i @ +2.500


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-' :"^^` '^`
View: -0.759 +0.000i @ +2.500

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 midget, largest midget, 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:

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 :


-0.081 +0.625i  +1.250
-0.081 +0.625i @ +1.250


-./ 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^ _['
View: -0.081 +0.625i @ +1.250

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 midget 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) 1987-2017.     Mu-ency index


Robert Munafo's home pages on HostMDS   © 1996-2017 Robert P. Munafo.
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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11