Favorite Views 1993
Robert P. Munafo, 2000 Oct 24.
19930104
RF(N/2N-1B1){FS[2]}xMJ32
mp24.jpg ^^vc,^\c"eded_a`./`./" ad* "e,'~e_@YF@@%bC@@er`._"^ _ __'~vmrYd/@@@@@b)C(aF__/"^ _^~v"Y/@@@@""*@@@@@@*@__,- ^`vd~^/@@@@_ -@@@bb\)d@__- ^~()d@d@@^ '^@@@L@dL,_ -`TY@@@@^, .m@@FF@*._ -^^Y@*@@@@a_ammad@@F7m"-__ r-^\7*CYYYY@@@@@YCbm(^-\, __"^.r^^"*bCe/e"v^~_'"__^" *`--" "" -`-` * "- '` '"-- -0.749 969 252 062 344 254 958 +0.051 215 642 132 179 378 170i @ +0.000 000 000 000 000 004 336
Views used to evaluate the DEM/M algorithm4, 4, -1.3642, 0.0742, 0.0625, 500, 0.50
4, 4, -0.74768, 0.08752, 0.003, 2000, 0.50
Series approaching the Avagadro mandelbrot
4, 4, -0.745990592, 0.105487722, .000000953, 2000, 0.30
7, 7, " " .000000119, 5000, 0.30
4, 4, -0.7459905921900, 0.1054877101360, 0.0000000000350, 5000, 0.30
(haven't finished this yet)
RF(n/2n+1B1){FS[2]}xmFS[(1/2B1)FS[...]]J2 n,m,"..." unknown
An approximation of the Avagadro Mandelbrot found using SMZ.
(an embedded Julia Set near the main antenna of an island in one of the
main "shepherd's crooks" in Seahorse Valley northeast)
4, 4, -.730680491, 0.224426668, 0.000000119, 1000, 0.50
19930108 Test image for period query algorithm
-1.769 110 335 +.009 020 488i @ .000 000 180
mp25.jpg . ,^.d*C"$@Y* '```:_($La"**$^^mre_', .,' \, -.(("*`d .-m' ^Y/@@@(@- `:\-^"Tc,~. '\, -(d%\*^^^^`^'"\ ``:'"^~ ] ^*@@r/(,-` ^. .]b'__c_ `_, . c. -(m_-`'^`'""b'_,- ',,__~(Y\r@*Tv/- 'mm__)d__a--^ -"".__/F.Y@\;_, "^""^%bd@@b$-b)^- ''; `'' ^L.%'"r, .aFdY@@@Fv(Y`` .` '%*bc -"e,%%)C'-, ,,` -., \.: , '[Y; -'F"(^^ '-. _ ."^ --__._dm-rme,,'%[ ' `-.ade` vm@/^_e__^Yc]$[ , .7"`-. -^'$Fv 'a()mdb@/^- , -Lme`` .-Y/e,"(@@@@@@m; bc- ___,--^'Y"`-__ ` ]^T*"r-/@@@@@[ '"_.---^^ ' ' ^-_ ..-`/[\$*(; ^"*". 'b_ .,'` -Tm,'^^` ./ '^", . .-` ^-"bC/_, ~ 'e_,` ..- --''^;` . .. -'*""v(.aL_. '' ].,:~,.__, _~ `_"dY- 'e._m@*C"/e__, ./- ` ~, , - -_:YT-^,,^~*br, _-' ~"` ` '^` ^^^^^''^ ^` ^ -1.749925308450 +0.000000139732i @ +0.000000002288
19931219.0017 Exploring one of the cells outside an FS[0]{[2]}xNJ2
mp26.jpg -_ ./ -me - ."` _" --_, a` / '`-._ ./_,/` -:` '`/F%@$L-` _ [ _ -'F@FL@`., ' . '` ~ .-` ,`'\` '``\_, \:_eddv_,__mb(dba\ _ _~` '`--'aF-^-`mrd@@be -"^Ye ._.,-- ./ _vrY*md ^*"^F`` a.:@@\^^' -` _TLv-~`-, _./"'^'".^\@`- -'^ '\/:m,,""'` _~.-e '-Y^%_, ':*@@[ /_ 'd@@YCam"^ ^^^ _-` ."ea'%^\mvm('.`' '` .,- .`^^T"Y^"'- '\, v/ / ' -, -aa` :` ':, .`` ' '\e_ .-` -**, ."- '", '` :-; ` -1.7499253081018 +0.0000001389187i @ +0.0000000002861
19931219.a The most asymmetrical shape found so far! Three of the emerging filaments go somewhere (unlike 2 for cells, 4 for mito's and 8+ for nuclei as heretofore seen). (The 1 o'clock filament goes out into space; the 5 o'clock filament goes to one half of the cell, and the 10 o'clock filament goes to the nucleus (seen here) and another 3-mito which connects to the other half of the cell and to the origin.) The nucleus is also unusual, in having only two emerging filaments that go outside the cell.
mp27.jpg -_ , - ,,/a:,-,, . :_ '-, .:_d\_edF"F^@b\\_\., _~ , ,:e@^*~'(FF" 'r--~"~@m- ,` . . _, '-vaF;^`/__ .~a-~ .:ae%b/___d_d`. ..-` __, --\F;"^` '`'",` --@;@@@@bd`"d^*v,' '^--,,"]7._ea_ \, ''^^'@%b" '\:""\c-^ , ,:.\@@@m$[ '[ /` '' ./''.;Y, __,\-` -__:_mF^m@@F7^,_ -abe,- .` :a_._@@d_:` .a)"$ *vm(` '^---^"(..- :am_,_e--^'"/ '^^/b`__ --d/,', _ -vmm@m-^*(` '`-rL%Y`- -(F%.'-\, , -La,-Y@@"^- ^ , "/YC^---- ^'@v._,_]v__,-'^'^F*; '` )_,--,__, 'b-vL, /\@"^ ._.7@@b^ ^F` .` .-^Y*" ``-.b@@F\a)(L ^` ^` ,@%`__-` ,._ ." -, -'@Y@@YF^`/ .-"@L_F^, \F@bc(,,, \ '^^Y""/[_ `--,, :"*bed\_'"@@@bF@-- ._.e_, .___-dL- '--__ _/^ ''~"T^^"7$^"""` .-*\` ^d\_^dF-., '` '` ` ` _- ~"Lr\_-v-c :mmb,.)d@";' .^ '`'"*v/me]/dF*"/F^^` '-, /` ~ ' /'^^/^ ` ' '-, :d :` ` :, ' ' ` -1.74992530818006 +0.00000013899587i @ +0.00000000003576
19931219.b The nucleus. Note the four 3-mitos surrounding the central 8-nucleus, forming an intermediate annulus between the 4-nucleus membrane and the 8-nucleus membrane.
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19931219.2014 A cluster near the top of the cell in the view 19931219.0017.
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19931220.0012 The 3-mito on the right in the view 19931219.2014.
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19931220.0040 Approaching the center of the 3-mito in view 19931220.0012.
mp31.jpg ^:, ] .-` -, -__]_ .- ./` . .'\d-*"FTd_, .-` -__ LmF"F(_^^._LY.C`. ^$/b',--", '"@@@7bd.-^ ---@\`.__ ^va^'^" ]"*c__._--- -^*e@d@e` -,__-~c*@e -__,__e___e___,--.)"%F` ./",_e,L@"-- ~ ^ `^ _%Y\.____( v@@r"^` _:~b/._e,~c-m* ^--__, --^ '"\"TYb(""`'` '`^-.._., .[ `' '\ '^^`^--/- :` :/ , : ._, , 'amb/_, ^^`^'^^^T;$@r ._'@\dL^^^^^--"-- ''F"`- .a, .` '` -1.749925308304871 +0.000000140395822i @ +0.000000000004468
19931220.0107
Zooming in a bit closer on the top half of the previous view. The lower shape is a normal-looking mito, but only 2 of the emerging filaments go anywhere.
mp32.jpg ' ] ,, L T` .- ._-^ ', ] / / / , _-` . T ,../._. , ] .-_a_L_La_` ./` "..)mvmd"FY"C"vL-]._b""'",^%-^$ed,_- _, __ -.m*_e^^^_'^^ _.%$mmCmv_e, '\,/"*`7@e-' ^--_`Cd,, `-^ ../FmY@@@@)$b- "["^^^"FC-- ,,.e\@@/- .- /Y\e%@[^"""' . aam/@^a_"--~` ___/*['"* `-~-- `'-^ 'c :d,_."T@@Y_, _-d;"._ __'Y-., ,T.e,--^^'~- '"".(b,^ ._d@db~~-` '-,., _,_]r`~ '~..,-'/@_^^^` ^ ._b-:/ ..._, -"\,.-^`` 'e -_. T*`.m/*^` ..`TL/,-C@$c,-' -"F` ,e,\dYF\m, d__^$`--.,_ ` -'"*"F@@@b, " '-F"@@@@@_*`__')mF"-, '`` .,,^`d/"-"' ,:_ '^*m%@Y^"vmm)/"('-, ."- -^ba_._.--*^^-.____',\@`~,' - ~, '-- :,-` ,-""Lm;T,vmae ."_,Tmr"- '\ ' /'^"rY-(*\eCdF7"^'\ 'L, ./ - ' ' [' ', ~_ ' -[ \ '-_ :` ' '`, '' ` -1.7499253080528 +0.0000001389312i @ +0.0000000001429
19931220.0124 The 3-cell in the view 19931219.a
mp33.jpg ':c ~, ..,'..- _~ '-c, v.m;mY"@bF~m,~ ^r. -.F~^`-,"--^^L-` '^--%Yd$, ', mmcF' , -_aF@@@^^Y-^/Y@@^ ` ----(Ce'' .'_,.'./[_, -Ym%/va'^^``""aF` _ -, \'Y@,/,'@@CaF*-'-- ^- '`-, ..-~ ."^F"F`-'' '- '" ^-.__,.-'` .` 'L ^- --:@CL@r- ~, '\, '^Ymd*` ~\ - _/-` - '-, ."c _:e_mm(F--(; _~` ^-c '\, - :*^`'@*[ *-vd@_. ' :dC^_ ._%c-^^-.%@-_ ]@b _, m mc'%@, ^ _d7@@[ -@, @@C7^ .,] **` **YL ^--__ --(__\, @`:-_@L^ '-v_ %"\**)d*^^` ''-_, '` '` ' '` ^`` -1.749925308046610 +0.000000138935042i @ +0.000000000008936
19931220.1017
Approaching the center of view 19931220.0124
mp34.jpg '-,. c ]- . _, "`, 'c ',. ] . : :- ._~` '-, e _'edrbdm/_arde,.`, . ._-'` '\, .':m**"_^'*@@"'"-Y"b),' _-'' '.,-aF-`^'`v_a'_.,~^^'-T@r` a,- -_, "._\__d:Cmre- -*^^ a___"[.-^ '^-,.m@"^:r@@F)*` [ ;@/@@@rvm_`_-` ..:r*`a ''Y-"'-, 'F \-Y$CF,'_@mc__,,-- . d(/^`, '. .\_,`m./ ./` ''' :L,YmL ^^'^ $@@-(\____ .. `aC^T%"d___mL_, _,' ''/;^^ _dd@^` .^` ^^/@^)'b\a^_@^,^ - ^^`/C-v@@Y_____,, "(e/" ,,, .~ -'^T^^\ '\, -,d^"[- ''^`` --''`/m_`,:b@@c/^ .- ~,.dmLc ]"e(/(^- .-''*Ye$@@@Fm- F .mmd@@$`_rL/[^-, `-\@/*""` :_^, ''\%@@"^^^^^-, '`- ._-` d"@-__,,,-'"'``-.___.mF-'\, _-` ,~*dmm'` mmmm :"_,CF^'` '\, ._-^ ' `_`Y*)\v""-(*r"( ` ~ `\, "` /` ' ' - ' _ `_, '` ' - ''`\. '- ^\, ^ '^ -1.749925308046575 +0.000000138935007i @ +0.000000000001117
19931220.1038
The 4-nucleus at the center of the previous view. In the center is a slightly distorted 4-nucleus with 6 connecting filaments, and 2 3-cells at 3 o'clock and 9 o'clock positions.
mp35.jpg T` ' '^` _[ -a` ., '^ .r` `v , . . .- .-` _ '\ -.L_/,,' ,...r :~ ./` ~,, ~\:arb@^F"\%bL-"d(mm,; .- / ^-, -.d(-.b- "*Y@$- \`^CLe\ _ , \ _-._- `-_^@L_, ', F _vec"*TF,; ._`, :_rd"Td_- .. aa/@@@\,_adm`,\d-~^ '^'-mF-----@@r--^@)m:@F\ .%FC ^*F ,--@@``^ .__,.)d`` \ '`^^"^` ---- ^m(e, _,Y@(~:vm^^^ab@Cr"` ` ' ., :]mc_,~-'` ] ' ~, "*"b'--, \ ` '^YF-.; ./me\e .d--v.bF- '-._ ,' :""r_edFYY@^,/,(FmY"-, '^. .^ / `-' c'^^"F"^ \ '",_ .-` ' :` - ~c ^\, /` '- ^_ ] ':, _] `'., ^ '^ -1.7499253080465709 +0.0000001389350552i @ +0.0000000000002792
19931220.1110
A closer look at the 6-nucleus, showing one of the adjacent 3-cells. In between the 6-nucleus and the 3-cell is a 4-nucleus with only 2 connecting filaments, as seen in view 19931219.a
mp36.jpg .mm(b-m"\- .-^ ^m ,\...,,., -./^_^%^_.a@-'` _ .F"%@%bL _7\m_dL '\/m@` /L$@F._mm"--- '^^YC%m7Y-* -- --:Td^`._^%$` ._- ^^^` -, ][ ')e~^_meb"^- . '` ./''"*F"`^ ' ^-, :ea_ - _` ./ ` `._ _:L@%\,**"^@*(;_-` '-- '`-_C^^^'\-_,' 'Y)m _.____ ' @d^^-(L@@F~_---^@; .m*` -%*\*@@@m^ ]@% .__ ._, -*m:^^'\d@*r~^-ve@-- ' %T@ _c ^][_mm/%^ ./^ -~@*-"*@_a-@-\ '\, _ . '` '` '`' ^-, _ .a(m%*"@_~` : . , .,"''^` @;:%-~"^m[ ] ^./\dme.-' -*me_ :m_m\/ ' '@%]-`v@@rm/., m%L__'(* ., -*%e'cv/^.:@- _-~"*-@F- '_ ./-^*Fa,vmr/(`~^"`- : ^m -^ ^]^T"''^ `- ' ' ` -1.74992530804660802 +0.00000013893504430i @ +0.00000000000003490
19931220.1125 Now looking at the center of the 6-nucleus in the previous view; an 8-nucleus with only 4 connecting filaments is surrounded by four 3-cells.
mp37.jpg _rdT*%dC*""b)m_/,. :` [ ,-`_: ." . ., ,`^`,'T^_/-`""^%"L- . _\a/m)mm"dma/_,C .~ ._,`` dr -)^' ._,/'Yc'-)/""-""_a- '*Y~(TbL.- _,-` -__." ._\a/"%%m@bC--rer, `-_m--'^'"@[.-' -:F, __@$ T7@@@@@@T,TbC, '` -@@@b\a_- __ F", `.7vm,d%)"@L-"Ld/`, 'c ,.,'FF`~^b_` \ ' (^"` ['^^"["- -mr)mc_ a-^d@-__ '; :[ ' .~ ' '^^"v^**e_, _\e, _ ', a` `e%FL_, ^.%",\ , -,.)m :,_" _:_La, )a)- %*@^^^^`'`--.m/(^`^^-"-----"*-_- `d^mCb.@"-'` -_` '", ` --^mm--^-^d@@@L^`---_, _- ]- [ \@$*@`YL, , . a-_, T _ '\ ''""^ /F)^` ; . aa"d)ee].._e__./ '\_, ..",mL---, " _\@,aamd@_d$C^^@b,.- -_F"-----/_._b"- ,m- -"\['L@@@@@@)@-'@"_ _,--` .. (_*@~-._, [ '~,, ''"""($(YFC%La*"- .~ .:em/c./mF"- ^- b)_,"'`:--em7("''YcL,`' ___/"- '@@@Fv(*^ -. ^*F\FFr"*'^-' ` -")(_rc%:-`._L, \r-\d( -, `' [ ` [ : ' .^T"Y@_Le$*(mLF\"'- '-, ' ' ` ` '`' ' `` ` ^` -1.749925423787 +0.000000208831i @ +0.000000004650
19931221.1143 2-cell on north filament outside view 1992xxxx.a
mp38.jpg '[ '- ./` \ c ..~ -, '\.,e__/ .-` '^, -., ^._eeCd-/Ybm, '\_, ':/^/'*"\-^`-*)-^' ''^, '--]\-`\_/'\d@LF[^ -- ''*@@) \_'%@`-.,, '`, , __-`'bem/m/"\` ^-v- ., '.ee,.-^ ' /''', \ , ^]@\~$e_ ` -, , \.e_`. a,-'"/*(, ^ -.,, `-)-d"bd(-_"-` ` ~, ^^-_(@d^';-Ydm__ `e- -_://@Y`.-".^~$,-- `__ _._Y@\d`,".__.Cd~^, '^e '""m^L,*@F"F\ `-, -_ a~`:"T""`', '~, _-` - ', /~ ]- 'e ` -1.7499254244972 +0.0000002089229i @ +0.0000000005813
19931221.1151 Center of view 19931221.1143. Note "pear" shaped 3-cells.
mp39.jpg '~_ \ c ] , .` ..v` ':, -,.__a_L__,] ca`,./` \/'` '-_'a/*/%L-^^%b_-*"$7^mve,` ,~~ -,._mbbb-'[ -(/@@Y@` `r-'*\/.-'` ^--,_ -.@@,^^'.m, ''- ^ d[,'@@/m,__ `.dd""e---*^-._ -_m__,-~^~[,^."Y[- ___ __'-@\_~ ~Y"- ^'r-b)-^^^ _-@/`.:a_e_, : -,.. 'rdF%__ -'Y\v($%:b- : .%("*m_.)d~, ----------"""@@@dLL___-m.- . -'b@@L(m*- -.d"b@F@Te ''"`^^^^Tm@@@\_%^-^----------c . ^a@['*v@md`' -[ -Yc$Cd-(v._ '^^\@"[ -'- [ ' ^^^ /^C___ .__%@m,Le, . -,b(_, ._-^/@- --''` -YF_~`'\_,.-^^^*,` ^^-m-^^'\"@;---__ --'Fda@e'''^ _,,[.e, '7-mmm.b/., ` .-:@F^._. 'd@@@@T) ..__"YF^; _/^ '^*@am.\m_$FFY%L.(]m/rF- '-, ._-` ` ./'"^^"' [''^T^"',` ` ~\_ ..-^ ./ ' [ ' ~, '^-, /~ ' '[ ^ '-, ` ' -1.7499254202715 +0.0000002085255i @ +0.0000000001453
19931221.1158 Now looking at a 2-cell on the filament to the east of view 19931221.1143.
mp40.jpg Tb)^''e_/'"`./^Cc--' 'FLd@mL '-e-^^`%(c` ,,-:F*^ ./^-amc)F^^^^ :,-^ TF@ca^\d*YF%^ ^ _ a,-~ ' '^"\dr)^` ~., , __(( .,` ` [ ' `\, . _.-\^ -' '-.:a,_.--^ -*@" ----`--- _\mm- ._,-^^'F"'._, . ..- ,:r^` '~,, , : _ .-` .:e-^ '`. /:a("-_(. _, , _ a,-' ' _ ,L/@m'~d%^7m\ .a,--^` .--" __,-bY`Y*"_-` ./$)r-'` --@C-_.-*`,.'"@@"v;- .._,-(@`]`._,."",'\]\L`--, _-^"` '(-/e/d@rc :*_m$F` - ''\"@%\/dv@Y^-_ -` ''"^"^`` `-__ -- ' \ ` '` ` -1.749925420276457 +0.000000208530003i @ +0.000000000009085
19931221.1209 The center of view 19931221.1158. Two pear-shaped 3-cells surround a central structure which itself consists of two pear-shaped 3-cells surrounding a tiny 4-nucleus.
mp41.jpg ] / ^F` -. ]` `\, ', ] a ._ '-, \./___/,'..,`,.` ,_-' ,.-/d*:)":%)d@@""Y"mc _,-` --\_:/F*"./ ^)*F7F 'C v@e;_ .-m%''^^-_ [, _.--\%/@c_,- e_,_,_ , -@[mvc ^e,: \b-' .__~YC_ ` ^^^^^`^..@@@)--~"`-_m--.__:C@eF` . -"T@'""` ^_C`^:*^ m@@YF^^^'^--v----m-, .__"Tb\,_,_,-`^~ ` '\,,''\(@r- -"*)m(^^ ,_,_, '['^\@*-__ .,-]Y;:-\'"d@@d` .[/Y@"^- '` .e-' '^7\""*^7*vmear)(`'\, -- .~ - [ ' \ '\, ]` ` -\ :` ^"^ -L ` -1.7499254202769545 +0.0000002085309615i @ +0.0000000000002839
19931221.1212 The 4-nucleus at the center of view 19931221.1209. At the center is a ring of 4 3-cells, with a smaller ring of 4 3-cells inside that.
mp42.jpg ~_ ", ,_'_.aa__e'_ c , -,]` , _` '-, _ '\/v"bb@`\$L*"*vc`a/rv"drm_,/` , ''_ ,aF^^d_/`\,- -:F@@@mme ^(''mbm(m__-` _'-,:*^,, `'*` ''"*T*)F- :\_d_`a_*be, `-_:ded/"dd@@Te ]c ] .^` ^"Fc ,_ v,edY:^-]/*F"^ '^ ' ,, :~ -/(b([ '--_/@C^', ^"^ '-.,'ee(_ c .\-b/` `""b@[ .:mY@`-`, '\Fb*" [ '7"`` , ._-`"F- --._@^___-"--,, -\ -,_,` , '[. _,- .~ '@\~` '`-, , `\ . ^*F ` ~@@^` :m"m` . 'Y$arv(- ad)m_,.aec ^._/rvmv(,_,-,.,-"/F^^^'^` ---~^@@b"___,--"*" ^^-"^-/@^\dmba:bL_.md, _,md`C@$F , ^^-vF-d@F^$b7c@e_L`^`^^`^ :F",``` ^^^^^:be-~@;\7FbY*\\F- ^^ _m.._-.- ^^$@d"., ..../^`_,^"(L/Ld$-^ ^(@,^^:@Yd- ^'\mm,'(_-^'"^^:@@@, '`a_a`''``-, -, -, '"^-_ -^')C* .~ `^ ' _/^`*(` - ~Y*\, '~. --_, -"*$^^ ,_a, a/^ -` ._^ ' .._ar .--''v(c,@@d@c` %/@@/ ) -~"d[^-._ .,. - ~""^T@*(@; _-`'^`- ` [ ^-a/m(/ _-^-Y_^"` /` ' -\ a])@@@F%_, '` '^'` '^^ ` ' ^`^^^'^ ` -1.749925420276963050 +0.000000208530962530i @ +0.000000000000004436
19931221.1215 The 8-nucleus at the center of view 19931221.1212. There are 16 3-cells in two concentric rings; they are now substantially closer in size than the sets of 3-cells encountered in previous views.
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19931221.1232 The 16-nucleus and island µ-molecule at the center of view 19931221.1215. The ring of 32 3-cells is quite impressive, and the next-inner ring has a really nice "texture" at 256x256 resolution.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.
Mu-ency main page — index — recent changes — DEMZ
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2022 Mar 28. s.27