🚀 go-pugleaf

Tim Wegner <twegner@killerbee.jsc.nasa.gov or twegner@mitre.org for now>
sent me email with these questions.  Apparently he was unable to post so
I will.

> At very deep zooms is one increasingly likely to encounter copies 
> of structures that exist at shallower magnifications? Is there a 
> point to deep zooming? I still believe the answer is yes. Even if 
> deep zooming always eventually results in self-similarity (don't 
> know if this is true) it is possible that the zoom depth at which 
> the self-similarity starts is arbitrarily large. If so, there is 
> still a point to deep zooming.
> 
> I posted this question in SCI.FRACTALS. I'm not sure it got posted, 
> I don't see any answers.

Of course we should DEEPZOOM ;-) but it all depends on what you want
to see.  If you get caught in one of those tornado like regions around
a pre-periodic point you will see self-similarity.  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.  Each with delicate 
filementary structures attached everywhere.  These little structures
contain a 'genetic' history of the larger (less zoomed) structures
you were looking at before.  Now you can either zoom into one of these
attached filementary structures or dive into the thick of it next to
the large island MSet you are next to.  If you do this you can set up
any designs you want by selecting elephant row (the cusp) or its
seahorse cajon (its equivalent to -.75) or even one of its branches (its 
-1.75 area is nice), or even one of its pre-periodic point tornados.

Each time you do this - target a  locally largest island MSet - you
seem to go through a layer so to speak.  After several of these, you 
build up an interesting filementary structure history that can be 
very nice.  I'll post more on this sometime.

It reminds me of the dust jacket descripiton on Poul's SiFi novel 'Tao 
Zero' where the ram jet space ship's reverse has failed.  "The sound
of a basso gong went thought the ship as they passed through another
galaxy".  This is what I have in mind for an awesome mpeg into the 
Mandelbrot Set with something like DEEPZOOM or FRACTINT.

Warmly, 
Jay "Not tonight honey, my ram jet is still stuck" Hill
PS. If you have svga256.bgi for MSDOS SuperVGA, try this:
-- 
#include <graphics.h> /* hilljr@jupiter.saic.com (Jay R Hill) */
int huge D(){return 4;}long e=0;main(){float g,s,f,r,i,w=3./1024;int m,l,u,b,c
,d=0;installuserdriver("Svga256",D);initgraph(&d,&b,"");for(;e<393216;){u=(256
*(s=(r=w*(m=e%1024)-2)*r+(i=w*(l=e++/1024)-1.125)*i)-96)*s+32*r<3?1:16+32*r+16
*s<1?2:0;if(u==(s=f=0))do{g=s*s-f*f+r;f=2*s*f+i;s=g;}while(++u<191&&g*g+f*f<4)
;putpixel(m,l,31+u%192);putpixel(m,767-l,31+u%192);}getch();closegraph();}