R2F(1/3B*)
Robert P. Munafo, 2023 Apr 17.
R2F(1/3B*) (abbreviated name: RF(3B*) ) is a Branch Point in the filament structure of R2.1/3a : :m(e(,.-:/^` /\:@,/"^^"%:_c <------- R2F(1/3B1)S --d, _"- _,,/@Crev``\_-- .- ' '_/-' "c__ :,r~- `" -^~__"^-' 'c %]er- '^:-` , '\_ _ _.m ,_'[ _ 'e\^ :c 'v` .:@^ -`"^^^\/d/%` ., R2F(1/3B*) ^-Lc -,.-_b.c _aL, _d%Fv"__.--` | ^v-v:"'@_d$--;` "- .,_aC``' "-, | .,, ., -,ea^ '`"e'^ ' -" '' "Y, ./ | .b, -F, v/'`' ` $-_ _r*aC_r | ,d)-(%F-\e, .d`'),_, v "eY."*- '^- '-- ^ ^$"L,.:e-"T'"- ^` `T^`' ._^@^, \ ._^v@m"' \ . _(),^ \ ''v\ -~@'^ .,., \ .a,_,_'Y_,"_La, _r/~^` > R2F(1/3B0) '^"F^*^`'%@%%)""Y__,. / , , ,^.@_~^ ^*^" / '~vL , .d$.m@L/-- / '-T:)` :, . -d\-^` / .ae ._ -",- Tbe.Y-,'-\(@Cae .va` 'ma ..F_ :-_@L,m,,,T) _ `^/bb,-_/@ba,:,_C___ _a,:F"";- '^^'^^'^^^'`` '^' ^''^^^^^^' ^^^ ^' ^`^` Figure 1. Part of R2F(1/3B), showing locations of R2F(1/3B*) and R2F(1/3B1)S . Coordinates: -0.0981 +0.9691i @ +0.1500
Three main branches or spokes are clearly visible. They are:
R2F(1/3B0) (which is labeled)
R2F(1/3B1) (which extends to the upper-left)
R2F(1/3B2) (which extends to the upper-right).
R2F(1/3B1) is sometimes called the "main branch", and is the largest asymmetrical primary filament in the Mandelbrot set.
A little-known feature of most branch points is that the branches actually spiral in. As you zoom in towards the branch point, you can see that the angle from which the three branches approach gradually changes:
''d._d\a"`` _. _aa~C^~vm_ dL[- -_-,$*- '\, '^ .-c ,, ^/be _a$*,- '^^"mb(,, '\c _7"- -`^*Fvba_%\/^` , _ _, .,a"\^^"*-@e,mL $_, ,-dmF` Tm_ ''-/Cv__, '\b(L , --%aC' '*La_ ^ _e/`^` .. '\c.mmF' ^ ^7YL, .-aF" -_, '^\-md$/"_ , ''^ a)*' . :, -d- .e .,e/\^^~", @-v\e_/,__'[a . "d..$` . .,va"` '*- *e ' ~"^^%Y--(/:e_$/F__..,-[. a_*Y^- :ba- '`'` ` ./"\,^^*["vF)-(b._r^` <----- R2F(1/3B*) '-[__ v"^ -b_ "') ' "[_ --Y; ' "F^ ""C` ,. -m/_a.- ' ..."cr"`, ^^d^` _dr"F^^ :-*_ ^^ .7L- ,,_a "- -~"e, __/b^^` _..._ ^*c./"^` "^T^*'--)":aa_a__- a:m^ Y. '`'` .ddm""- ^Y., -` `` ""Y^ ._, ._."e_-`, , , - ._:)"C^'' "L,/.ae" '^` '"F._ .,.,a_a*F(_, '`^^ ^ `'^` ` Figure 2. Detail of R2F(1/3B*). The bottom branch is R2F(1/3B0). Coordinates: -0.1010963638451 +0.9562865108091i @ +0.0000000002793This spiraling continues forever: Each branch twists an infinite number of times around the branch point.
revisions: 19990202 oldest on record; 20230417 spiraling is "little-known", and "main branch"
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 Apr 20.
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