Proceed to Safety

Leavitt, Jonathan    

Robert P. Munafo, 2009 Nov 7.

A Mandelbrot explorer who has discovered many esoteric and beautiful forms within the higher-order embedded Julia sets, at extremely high magnification using FRACTINT.

Most of his Mandelbrot images are very exotic, including such things as reverse bifurcation. Here is an example:

`^--^Y%.L,^"b,',-'_Yc^` '`F^b/*^^ T *YLc.,:ad/b'r^^L@)- . ._d)br '^(Fv)dF^\ _:-mm,,'.e_/.'_,/'"brdvF^,_:"'$^^-^^` - a_ c . .dYL'", ./_.'-m/e-.@([-:$CY\.d@@~\]__`, :^ abFC_-- .- ; FTLL,,` \-/F` ,`"@Fd,^@bT*dF@`;-/b"@@\d^`-/@@_:.L_.,"LL- /.-._a\ "d^d^@mmm"*,^mda:@r@d.-"@c/'@/-^'b-/@^-\':@(@b"^a*- /*"b\)(-@`Ld dL,'['^ -,/ ""@CC"F]L~.^%TC"%b\'d`(@*-`,b@--$)*^^^-avm^ ''d-v_`: `*m_^---~CYm[c-^*bmvTb,. %*LL'$/(L(@-'.\$)c@Y/^;:/Fm/`\_-` .mbeF ^^:@%,:\$'*7@\/-^`*@.Yb`: .d*@F"_dC^':'/@^/F.:amY^:@mvdC@---/``- .^_@\ad$F$(^"%$\mLC@;"v\;: -,Ya("@c': -@F(@^*"L.d_"""Y^^`^.'@_^. d^*_ -'''^^""rm$CeL7(`-"FL..-]C-bF. ,)@\`r_mC("C'--_^/.Lv)m--^Y) '__-@@]vd..'_'^```^(^Fe%]7)eaa*('Y__v"-ddF^L/^`..-__/""`mF`,_.-" ``^_'^*d@^b(e_dc/e ,'^`'*b`^L)ba@)d_/m/^`^.- ~.Ld7)d\%%@@-dmL : C,-_rr(F\dmd/r(C$dve_de__F-b@@@@@@@@@/\mamdr-@^ea/"^"`~^""^"`^%m @b-~^"^^"'~'"^d_)/'`;~^\^r*@@@@@@@@@b)/Lm%r:/-."~bYeLeLeed_Le^*C "--__/eLaL_Lab((^$F""F(""bF^@@@@@@@@F`FL-'^`^^"))de$^":$aFFY[^^% `_d^")F\d/^/_br/T`- ',vmC@b/^F"@F*($d:")C;--__'-':'^*FL%@)a,,,.. b' -_r(Lbb*)`~_`--..@m^Fmd("^Tm'dF`FYe)^*@evee%.-._-`,'T*\*` ._ Y@,-^**F^''-.::_m\/^7_"^$F-'.-@v;@v` `'Ye-\med\d""(-m\a__e`,d:mF ''@-`-._e("")"F"^@vmF"^F-, -\F\~^@\`,`:YC-a(^"^*(e\mF"d$*,'@7" --$@`^.*)v*b@()F*^``@Y-@~,`,\d"_e/^Y-d_`:YL`7YF-;`^b"\_`^ ]$_-- /%T^`_,- ;:FYmF-'m\mY"()\ --aY7:/YmYYLr_`.'LL(^b__d-"Yd"^^-m"(@a `_^'^F.__,'*^``.)/$$-$F- --a\/(F:-7d$'Cr- /]^*d@(7v,,`/\__,__d%^ _T)F"F^"*\b;.'@C$"^@($"--$a*_"@F-'($\%"b,--'@)b.`("^_\Y*^"Y_La.\ ("".[ '.'-Y7^ '\ \~@bF',\/@(Y_Yb).(@T@mLFe`'/bd`-, .((L` ','.'@d : ' ^^aa*(`__;_,:^` -^@b*,`@[@(-7L$F,]*F"\_.-__'v""@,__, ', " ----raL^:`./L@)*(Ye_''`` ''^`c''"^`, .'m@*("(CvC_"*\,_^ ` '**^"-'`"*` ` `''"- ` --"**""-- '-~**`' ''"'- "^'*-^--- -1.749078161505201731679124545156633037 + 0.000005509919066290966025130985672062 i @ 1.926e-33, Nmax: 20000

Leavitt created many stunning images from January 1998 to (approximately) 2001. Some of his stunning images can be seen here, and the Fractal Foundation has a few other Leavitt images on their website and associated media.

A partial snapshot of the old (now-defunct) website at can be seen here. Two reverse bifurcation images are here.

My investigation of Leavitt's images in 2002 led to my discovery of the exponential map coordinate transform as a tool for understanding the structure of high-order embedded Julia sets.

revisions: 20080228 oldest on record; 20091107 is only partial; 20100923 Fractal Foundation website change; 20101205 Add link to exponential map

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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