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.

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: 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)

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


Colloquial: utter west


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



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.     Mu-ency index


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