🚀 go-pugleaf

In article <1994Mar4.220538.10688@ast.saic.com>, hilljr@jupiter.saic.com (Jay R. Hill) writes:
|> In article <1994Mar3.213650.10380@ast.saic.com>, 
|>   hilljr@jupiter.saic.com (Jay R. Hill) writes:
|>|> A 90's alternative to chaotic Mandelbrot Set viewing.
|>|> 
|>|>                    Managed Deepzooming(TM)
|>|>                by Jay R. Hill, PhD, DEEPZOOM author.
|>|> 
|>|>     Welcome to Managed Deepzooming(tm), a whole new way of thinking 
|>|> about exploring deep into the Mandelbrot Set.  ... 
|> This posting was completely intended as absolute HUMOR and ... 
|>|> Your personal coordinates and magnification factor are computed by our
|>|> Deepzoom Coordinate Generator(tm) using your personal ID number ...
|> Not a joke, the program exists and is being polished up as I write...

When you follow the upper left filement branch above the period 3
bud you find a sequence of midgets with periods starting with 4.  
The branch, after in infinite number of left turns, ends at a 
Misiurewicz point (see sig for code to compute this) with  
coordinates near 

-0.22815549365396181921457201409912600673739835117450803237959798108441566+
i*1.1151425080399373597457646363150140681887780904679546036274680334810409

The period 48 cardioid, associated buds and cardioids and surrounding 
filements can be viewed using the following DEEPZOOM command line:

deepzoom 99999 -.22815549365396181921458337174522594168584633202 \
1.115142508039937359745738033504392908720827794353 8e-45 6e-45

The image center is in the cardioid but not at the 'center', the 
mapping of the circle to the cardioid component (like 0+0i in the 
original MSet).  Instead, it is where all the filements seem to 
be aiming, a point corresponding to -0.5 in the original MSet.  
You can see why I like this definition of what I'll call the 'midget 
center', when you plot this period 15 cardioid.

deepzoom 99999 -1.9999999862123215309672207934661990639759 0 8.22e-16 6.16e-16

Here the filements approach very nearly straight lines.  In fact, 
when you bring up the 'cursor' which is centered in the DEEPZOOM 
view, the vertical line will be very close to the vertical filement.  
(This filement, BTW, attaches at a Misiurewicz point corresponding 
to -.22815+1.115i in the original MSet.  

Warmly,
Jay "Not to night honey, I've got a midget in the cross hairs" Hill

#include <math.h>
#define cubroot(x) (x)>=0?exp(log((x))/3):-exp(log(-(x))/3)
main(){ double A,B,U,V,x,y; A=-17./(double)27.; B=sqrt((double)33.)/9;
U=cubroot(A+B); V=cubroot(A-B); x=-(U+V)/2-(double)2/3; y=sqrt((double)3.)
*(U-V)/2; printf("%.14lf \n",x); printf("%.14lf \n",y); }