Fractal visionaries and enthusiasts:

The parent fractal is a variation of yesterday's parent, with only the portions changed.  Today we mix the same 0.25 part of Z^(2) with a much reduced 0.5 part of Z^(-5) before we add straight C on each iteration.  The change opens up more of the underlying Mandelbrot set, which now is much more recognizable.  A large area of (-5) stuff still fills much of the main bay, with today's scene located in the Seahorse Valley of a partly obscured minibrot on the northeast edge of this 'stuff'.  The name "In a Vague Valley" refers to this almost totally obscured underlying valley.

I retained most of yesterday's colors, making only a few changes to increase the contrast between the outer grayness and the brilliantly colored fractal object lying diagonally across the frame.

This object resembles a Julia set of the Seahorse Valley type, which is not surprising, since it lies in the Seahorse Valley of the partially hidden minibrot.

These partially hidden minibrots pose a puzzle.  I suspect that the generating expression has a second critical point and that if Z were initialized to that other starting point, the hidden minibrot would be revealed in its full glory.  So far however, I have been unable to find one of these hidden minibrots.

The calculation time of today's image is a rather slow 3-1/2 minutes, making the FOTD web sited a good choice.

A typical early-May mix of clouds and sun prevailed here at Fractal Central today, with a brief but heavy afternoon shower adding interest.  The temperature of 59F 15C was mild enough to keep the fractal cats happy and keep the house heat turned low.

The humans had another dull but satisfactory day.  With FL growing less liberal as the years pass, we rarely disagree on politics any longer, though she did grow agitated when on the noontime news we saw someone in congress stand up and point out that the bible says gay people should be put to death.  But since I agreed with her, we had nothing to debate.

One other thing never debatable is that the next FOTD will soon be posted.  The only uncertainty is the exact hour.  Until whenever, take care, and liberal ideals are great.  It's too bad they are only ideals that all too often fail to work.  Oh well, there are always the conservatives to pin the blame on.

Jim Muth
jimmuth@earthlink.net


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

In_A_Vague_Valley  { ; time=0:03:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=-0.1784695159550038/+0.8587374874909367\
  /932803/1/65/0 params=0.25/2/0.5/-5/0/0/0/0 float=y
  maxiter=5000 inside=0 logmap=-152
  colors=000HIREHPEGODFNCELBCJABH9AF88D67B5694573352\
  2311100000000000000000000000000000000500A30F55KFFP\
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  zzAzzczzczzhzzmzzzzzzzzzzzz_pP`pQYkNVfKSaHQYERVIRS\
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  Kc8Kc7Kc7Km7Km7Km6Km6Km6cm6cm5cm5czKczKczKczKczKcz\
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  zcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzc\
  mzcmzcmzcmzcmzcmzcmzcmzcm }

frm:MandAutoCritInZ {; 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)+(p4)),
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=========================================