Fractal visionaries and enthusiasts:

We're making a little progress.  Today's image might not have a name but it does have a rating.  After a modicum of pondering, I rated it at a 6, which is actually a bit above normal.

The parent fractal is a near-Mandelbrot set, created by subtracting 100,000 parts of a rounded Z^(sqrt(2)) from 100000 parts of the full Z^(sqrt(2)).  This parent fractal differs the most from the true M-set in the area of the negative spike, which has split into fractal chaos.

I always wonder whether fractals based on such extreme input are true fractals or artifacts of mathematical imprecision.  But it really doesn't matter.  A fractal is a fractal regardless of the origin of the iterated numbers.

The passes=b is actually the fastest with this particular image, finishing in an impressive 4-1/4 minutes on my tired, worn-out old machine.

The weather did a 180-degree turn here at the Old Fractal Central on Thursday, when a gloomy, chilly, rainy day was replaced by sunny skies and a temperature of 66F 19C.  Needless to say, the cats were satisfied, but when Tippy went outside, he looked at me as if to say, "why didn't you make the weather this good yesterday?"

In my department, all the papers that we needed to fill out and sign to purchase the New Fractal Central have been filled out, signed and returned.  All that remains is to agree on the settlement date, which, unless something unexpected happens, will be February 3.  The date of the next FOTD has already been agreed upon.  It will be January 14 -- 24 hours from now.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


START PARAMETER FILE=======================================

FOTD_for_13-01-06  { ; time=0:04:15.51--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=b
  center-mag=-0.02640469166611007/+0.004068373541426\
  33/4.450919e+008/1/-172.5/3.98367388552284263e-006
  params=1/1.414213562373/-1/1.4142/100000/0 float=y
  maxiter=1000 inside=255 logmap=83 periodicity=10
  colors=000ovrotpmsokpniomfmmckiZfdUa_PXUKSPFNJAID5\
  D87IC9NFBSIDXMGaPKfSPkWVpZ`uafzelzhrzkszntzouzovzo\
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  pmSnmTlmUimVgmWemXfjTfgQfdMgaJgZFgXCiaHjfMkjRmoWnt\
  _oxdqzirznszrtzptzntwmtrktmithhtcftZdtZctZatZ`s`as\
  bbrdcrfcrhcmjchlccncZpcVrcRtcSucTucTvcUvcVvcVwcWwc\
  WxcXxcYxcYycZycZycazcdzagzXjzSlzOezNZvMSpLLkKFfKIc\
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  YKTXNSWPSVSRUURTWRSZQR`QQcPPePOhONjONlORoNVrMZuLbx\
  KfzJjzInzHrzGuzGszJqzLozNmzQkzSizUgzXezZcz`azc_zeY\
  zgWzjUzlSznTzlUzjVziWzgXzfYzdZzb_za`z_`zZ_z`_zbZzd\
  ZzfYzhYzjYzkXzmXzoWzqWzsVzuVzwVzxWzuWzsWzqWzoWzmWz\
  kWzhWzfWzdWzbWz`WzZzzv000 }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

END PARAMETER FILE=========================================