🚀 go-pugleaf

In article <1994Feb18.205648.13940@ast.saic.com>, hilljr@jupiter.saic.com
  (Jay R. Hill) writes:
> If you get caught in one of those tornado like regions around
> a pre-periodic point you will see self-similarity.

Follow the sequence of cardioids above the period three bud up
and to the left.  The sequence leads to a pre-periodic point in
a spiral path.

> Just break off to a branch, try to find a locally largest island
> MSet and you can find the whole array of structure shapes there.

I have posted 02281554.gif to alt.binaries.pictures.fractals, a
picture of the period 32 Mandelbrotie which is about 10^(-30) long.
The sequence is (for those who might wish to explore)

 p              Re                             Im
 4 -0.15652016683375506179898665078782 1.03224710892283180167160153243019
 5 -0.19804209936425384006706548935925 1.10026953729269853292946466130293
 6 -0.21752674703051102736891220156735 1.11445426587329273196477528116824
 7 -0.22491595128674005468532625520412 1.11626015745499183500126825424467
 8 -0.22733132304700393850020723485875 1.11588359859402312790906438800341
 9 -0.22800380192119768440593561256394 1.11546788192985807009468931540234
10 -0.22815164143855000105962532908523 1.11525874731625437467075180497712
11 -0.22816913033455737825914409091174 1.11517762946600472614870779890337
12 -0.22816402388442481254773547314825 1.1151512357871120510828460360341
13 -0.22815914494963267922362645982414 1.11514402267262310759199436509364
14 -0.22815677396428361530981906175257 1.11514249470941736215744240030232
15 -0.22815587332714247866717366366851 1.1151423411958116277129217944865
16 -0.22815558552315644808961321089189 1.11514241004226826652595546152242
17 -0.22815550855263108159568120988684 1.11514246716222284722700817563524
18 -0.22815549289168166313358642159102 1.11514249396830935731555596097925
19 -0.22815549163680663920717494619641 1.11514250394536590772360527215044
20 -0.2281554925322253512909550642675  1.11514250707688756197138804714047
21 -0.22815549319731556856424943014538 1.11514250789577121812967396959899
22 -0.22815549349959990133282720600253 1.11514250805508562105684202780953
23 -0.22815549360990878542334551974513 1.11514250806408643629140304957281
24 -0.22815549364391173034831426363938 1.11514250805273480892297383016298
25 -0.22815549365259618062956104965992 1.115142508045027862555012636284
26 -0.22815549365420261160997315103021 1.11514250804162740475671111807369
27 -0.22815549365424854012252068118215 1.11514250804041014487455664512442
28 -0.22815549365410736972499445466057 1.11514250804004171457292269370484
29 -0.22815549365401844991684724388258 1.11514250803994992821477773170794
30 -0.22815549365398028678543082111145 1.11514250803993389938200454331354
31 -0.22815549365396687998323940973346 1.11514250803993397968632052442503
32 -0.22815549365396289668839451272971 1.11514250803993570912551129479396

> Each with delicate filementary structures attached everywhere.

Try these parameters in DEEPZOOM (For a copy send me email).
DEEPZOOM 65000 -0.22815549365396289668839451272971\
 1.11514250803993570912551129479396 64e-30 48e-30 640 480

In this picture the filements are relatively very long, going out
in slowly curving spirals.

> These little structures contain a 'genetic' history of the larger
> (less zoomed) structures you were looking at before.

Each filement has n=p-3 barbs on it where n is the number of
Mandelbroties in the sequence.  This is because to get to this point,
we went past n branch points like the first one (branching to the right
ending at +i).

> It reminds me of the dust jacket descripiton on Poul's SiFi novel
> 'Tao Zero'

Make that Poul Anderson.

Warmly,
Jay "Not tonight honey, I'm at the end of the branch" Hill

int m,u,e=0;float g,s,f,r,i;char*_="-moc.cias.retipuj@rjllih=lliH .R yaJ\n";
main(){for(;e<3920;){u=(256*(s=(r=.0325*(m=e%80)-2)*r+(i=.047*(e/80)-1.128)*
i)-96)*s+32*r<3?28:16+32*r+16*s<1?35:0;if(u==(s=f=0))do g=s*s-f*f+r;while((f
=2*s*f+i)*f+(s=g)*g<4&&++u<29);putchar(_[++e>3840&&m<36?35-m:m>78?36:u]);}}