R2F(1/3B*)  

Robert P. Munafo, 1999 Feb 2.



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).

One bizarre 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 @ +0.0000000002793

This spiraling continues forever: Each branch twists an infinite number of times around the branch point.




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017.     Mu-ency index


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