R2.C(1/3)  

Robert P. Munafo, 2012 Mar 4.



R2-Name: R2.C(1/3)
Abbrev: R.C(3)
Colloq.: Triple Spiral Valley
Coords: center = -0.088 + 0.654i, size = 0.

R2.C(1/3) is the R2-Name of the two cusps between R2a and R2.1/3a. The corresponding cusps near R2.2/3a are the same except for the vertical reflection.

R2.b(1/3) (the bond point between R2a and R2.1/3a) is one of those points for which exact coordinates are known: it is precisely (-1 + √27 i) / 8, which is -0.125 + 0.64951905283832... i. These coordinates and many of the bond points with rational coordinates are given by a general formula that applies to bond points of all secondary continental mu-atoms (see that entry for more details).

The colloquial name "Triple Spiral Valley" comes from the triple spirals that are prominent in the filaments of the mu-atoms on the child side of the cusp. Features generally resemble those found in Seahorse valley but with one extra lobe on the parent side and an extra spiral arm on the child side.

See also R2.1/3.C(1/2).


-0.15490 + 0.65218i  0.00781
-0.15490 + 0.65218i @ 0.00781


  ,c_, )C` '.,,, dC_ ..a\"Y"`d_-___ FYd_/dYFFb"bd^Y/` -,.._ mCm@Y@"`_, '""@(,,._:v"vF.m,m., /Y@*@$(%7@c -TF^@mm)b"*`"/m\^` .\c. _. ` :d)@@@@/L_d@F@@@Y/L__, ^:@)L,.m^//m.Fa/- \,, '***CY@@e^^*Y^"(F@mmF@__$*mC@$@"^`'*\%L_._:d\rac__- '@@/YC $b@@@@b"*Y@CbF@b%$b,dY@$]r@e^*"dcC` ."\e.,,_ *` '@dY@` ' :@/@@@Cmd@(@@CCmrm,-d"bL:@F*"FFT, ^* ` ^^*@Y@) '^ ]C@@@d)d@d@@@@mv,-/*b,m '*"^` '^^@F@) '^'v$@@@\/@@@$@ ^*^` '^\@@@ `'@@ " '       m_ _. .,, @$m :@bm,/FL, vm_,_me, ._,,ae, __ ., . @$)_,:ee,dYC~"@d@`.._,_Y@F^T@@` ._.-C%FY@@` _ -C@b(%e $\edY_ F$("*@CYYC$@%@/Yb/*FCCC$d$a(@$-@d"7@(7\]C^vm@bLFb_d)%rd/adF./@;m '"*- %$%:Yd\@YF*@* :\%^)7/@Y"** ^@;F(L\("'`'^/7dLd^"* ^\$/mCF*"' \,.._^eFF" '"/r,_._^mF"` `"\_,,\/e~^ "^L::-am;'`'-(eF.dC^` ]%m-m `/d-(\%/ (C"/-()/` CL"`~`--. ./\:-"-'-. '-`^~~~- -``'` `~" "^`~- ~-" - ' ``` ' '   Figure 1. Detail from the west side of R2.C(1/3)
-0.15490 + 0.65218i @ 0.00781

In figure 1, the triple spirals are found near R2.1/3a in the upper part of the image. Each radical in the bottom part of the image has a shepherd crook and two more prominent spirals.


-0.156250 + 0.653411 i  0.000976
-0.156250 + 0.653411 i @ 0.000976


$$@@FL@dbF-d/$Fb@d*F*F^^ ._ :mdb__a@mFb ., Fd@dLY$@m/`77C@@*F@YF^` ._.m@b@C%@@@C%@$mdm/@brc F@(@dF$b@F\$T@YY@@\F^ .__@@b@d;@db%@L@FT@*b)d@@C` , @e@@F@@bY@@@@d$@@*- _,mv@@F*\^^* '"` ^F"*b@FL@@@CFvm@_, em@$Y@-%*@@F@@F* .,md@@**'` '*^Y@bm@_F@@@` ^@@%^(C$@d**^` .am@$^` _._aemm@bd@eme__ -Y*bmC@@bc bF~*Y^^^ ._ab@*"^..am@@***^""'""FYY@@a_ :d@mm^$b@` ^ .,mv@7*^ aad@*"`.__mmaem_,, `"(@$mc '^"md@@F** ._,$@@@`` .e@F^..ad**^^Ld/^^*@be,'^@C\- -@/bF@C_ __:@C@@^ ._@@^ .dF".m""^^%7*\m,"@@, '@@r .m@d@F@[ .d@/@@@; .@@` .@~am"Lr(%"*C7-^Ye'@L :@@* .:@@C@L . :badF"` m$@ d@ /Fa^/)@@d$eL@'@ @C -@@` .:@@@F^` "d%d@@%@m- :@@, (b @,Y,LL@@YF@(F/".@`a@F- .d@@@"` /mm@e d@Y*`%C@` 'Y@e'Ye'@'b7()(db%)*Ld*`ad*`.a@FF' . .ma__d@*** ]@\d%FYm@_ .,.'"b_"b/Ye"m%7----"^amF"__d@*^` ,_m_/@\b@%$@m*Yr@ ._.'Y@@@d*@CmF$@@bm^b,Ye^*md^*****^^.adF*^__mdmF*@"@/*@b**@@b"@* _@F$@@_v, '"@d@@@@@@'bc"@e/^*\\mmd"*"^`_am**^`___ , ^^^ "**@@@@)`_:d**dC@F@` Yb,'"@be.,._.a_ad@*^_,m$@@@$)b_e (L%@@^*Y*@mc@vd^` .$@L '^T@YC@@F""^.a/F@@F@@@$C*dFmm "@b** '^"Y` d"b@_, .d@$Y@@@@@(@$-@a/"ea_ ^` ]FF"@)___ '@Lm@@"@Y@*v**Y"_/@@` .,"@b$@@C_, _)mr@@@ :@)Ymd"*Yd@*"*Y)__ *@@@\ '*d@bmv@@YF@F~d@@,,^@m@d%_,ar)bF@r -@@*b_mm*m/Ld@*^"` *@@L^^'^**^C@@Y@@` 'F\d@@@@@"`_ '*/)@- _, TC@` _d%%^Ym@**bm, .:FYv,rC$\:"_, --*"-~*-*-""'*` --*"**"*******~~ Figure 2. The triple spiral around R2F(1/3(19/20B1)B*)
-0.156250 + 0.653411 i @ 0.000976


revisions: 19990202 oldest on record; 20100919 add images; 20100920 add link to R2.1/3.C(1/2); 20120304 add exact coordinates




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2016.     Mu-ency index


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