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From: dewey@mipg.upenn.edu (Dewey Odhner)
Newsgroups: sci.fractals
Subject: Re: lopsided baby, freckles
Date: 30 Aug 1995 14:45:30 GMT
Organization: University of Pennsylvania
Lines: 47
Distribution: world
Message-ID: <421tia$ln5@netnews.upenn.edu>
References: <41covh$m8q@netnews.upenn.edu> <1995Aug24.010028.16040@nosc.mil> <41kus1$7aa@netnews.upenn.edu>
NNTP-Posting-Host: picard.mipg.upenn.edu
 
Several years ago I looked at a formula that I called Dragonbat.
Just this past weekend I started using Fractint formula for the first
time, and in a relative of Dragonbat, which I am calling Dragonbat2,
I found some really bizarre stuff including an asymmetric baby 
mandelbrot (see lops_db2 parameters below or
ftp://mipgsun.mipg.upenn.edu/pub/dewey/lops_db2.gif).  I wonder whether
this is the limit of the sequence I mentioned in my previous posting
(if you remove the disconnected wisps around it).  It looks like
the buds could become symmetrical if it went a little further, except
for the filaments, which have different branching patterns.
So the symmetrical object I was speculating about does not exist.
 
Can you believe what's hatching out of that egg that's lying on the
main blob near this baby?  
(See ftp://mipgsun.mipg.upenn.edu/pub/dewey/wild.gif)
 
lops_db2                {
  reset=1920 type=formula formulafile=dewey.frm formulaname=Dragonbat2
  center-mag=-0.13879555450000000/+0.61682742800000000/133.3769/0.9997
  params=0/0/0/0/0/0 maxiter=333 inside=0
  colors=000Q3c<53>vlxvlxukw<80>0MK<8>eTl<73>Hh7GNC<32>Q3c
  }
 
Here are my formulas.  (By the way, these formulas don't show the dragon-
and batlike appearance as in my original Dragonbat program.)
 
Mandelcubic(XYAXIS) {; Dewey Odhner
  z = Pixel, z = Sqr(z)*z:  ; Start with z**3 to initialize LastSqr
   z = z + Pixel
   z = Sqr(z)*z
    LastSqr <= 4          ; Use LastSqr instead of recalculating
  }
 
Dragonbat(XAXIS) {; Dewey Odhner
  c = Pixel, z = Sqr(Pixel)+Pixel:
   z = Sqr(Sqr(z)+c)-c
   c = -c
    LastSqr <= 4
  }
 
Dragonbat2(XAXIS) {; Dewey Odhner
  c = Pixel, z = Sqr(Pixel)-Pixel:
   z = Sqr(Sqr(z)+c)+c
   c = -c
    LastSqr <= 4
  }