;     Date: Fri, 30 May 2003 09:11:46 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 30-05-03 (The Dried-Out Lake [6])
;       Id: <1.5.4.16.20030530091116.29e7e02c@pop.mindspring.com>
; ---------
; 
; FOTD -- May 30, 2003 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; I should have realized it.
; 
; I see from the Fractint list that the 'bug' in the program is 
; not a bug at all, but actually a result of the multi-valued 
; nature of the complex log function.  It turns out that the 
; mirror images that result from switching the (p1) and (p2) 
; parameters in the MandelbrotMix formulas are both correct.  In 
; fact, an infinity of other 'correct' images could be drawn from 
; the same basic formula.
; 
; I have a formula in my collection named MandelbrotBC1, (BC 
; stands for branch cuts), which takes advantage of the multi-
; valued complex log function.  I have posted quite a few FOTD 
; images created by this formula.  I also have a formula hidden 
; somewhere which raises a complex exponent of Z to a power, then 
; extracts the same root.  Because of the two multi-valued steps, 
; the final image has little resemblance to the starting image.
; 
; Today's image is what I call a 'dry-lake', a term invented by 
; Lee Skinner, who first drew my attention to these features.  The 
; symmetry is there, but the midget at the center is not.  What 
; has happened is that the slice of today's image has passed very 
; close to a midget, but has not cut through it.  By changing the 
; (p4) parameter, the slice could be moved until it cuts the 
; now-invisible midget.  This is the reason I added the extra para-
; meter.  But finding the skimmed midget is not as easy as it 
; seems.  The C value changes along with the Z value, and, when 
; the (p4) parameter is changed, the center of the dry lake must 
; be chased as it moves off the screen.
; 
; Today's image lies in the north branch of the East Valley area 
; of the prominent Mandeloid feature located to the northeast of 
; the 'fan' of the parent fractal.  The elements in this area are 
; very skeletal, consisting largely of inside points, so to 
; produce a good picture, I set the inside to < atan > and let the 
; iterations add up.
; 
; The resulting image rates a 6 -- not bad, but with lots of room 
; for improvement.  The render time of 48 minutes could certainly 
; be improved, and this improvement may be gained by visiting 
; Paul's FOTD web site at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or Scott's site at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; and downloading the image from there.
; 
; The forecast rain never appeared here at Fractal Central on 
; Thursday, and the temperature reached 75F 24C.  As a result, the 
; dynamic duo had an exceptional day in the outdoors.  They even 
; managed to stay out of trouble, (which isn't very difficult for 
; near-13-year-old cats).  Today is actually starting sunny, with 
; a forecast of sun all day.  It should be a good day for the cats.
; 
; For me, it will be a good day when the work is finished.  And in 
; order to finish, I must start.  So until next time, take care, 
; and beware of multiple values.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

The_Dried-Out_Lake { ; time=0:48:07.99--SF5 on a P200
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=mandelbrotmix2 function=recip passes=1
  center-mag=+1.28250208122812600/-3.009422644531135\
  00/4914106/1/95.0004599045420264/1.230095661228919\
  33e-005 params=-10/-1.1/-1/-11/0/525/0/0 float=y
  maxiter=1200 inside=atan periodicity=10
  colors=000JTSMYXQc`TgcYmg`rlcvojjrp_uvPxzDzz1zz0zz\
  0yz3rz9lzFdzJ_uMclOgdPjXQoOTsGVv7Xz0Yz0_z0Sr0La3DM\
  766A007306704C03G01L00P00T00Y00a00f00j00g00f11d64c\
  C7aGA`MD_SGYXJXaMVfPTlSSrVQvYPz`OzcQzfSziTzjVzmSxo\
  QurPrsOovMlxLizJfzIczG`zF_zA`x7`s3`o0`j0`f0`a0`d0Y\
  g0Vi1Sl6QoAOpDLsIIvMGxPDzTAzY7z`6zd3zi0zl0zo3zp7zs\
  CzuFyxJvyOszSrzVfuSXmQMfOCYM1QJ0JI0IJ0GJ4FJ9DJDCJI\
  CJMAJQ9JV7J_6Ja6Jc9DcC9dD3dG0dI0aO0_T6X_CVcISiOPoS\
  MuYLycIziFzoDzsFzuGpvIdvJTxLIxY0j70IC0GG0GL4GP7GTC\
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  OScQQxJVxGXxDYvC_v9`v6av4au7Ys9VsASrDOrFLpGIoIFoLA\
  mM7mO4lP1jS0jT0iV0iX0d_0aa0_c0Vf3Sg6PjALlDIoIFpLAs\
  O7uS4xV1yYCzSLzMTzGczAlz4uz0zz0vx0pv0iu0cs0Xp0Qo0L\
  m0Dl07i00g00f00d00g00i60jC0mG0oM0pS0sY0ua0vg0ym0zs\
  0zx1zz3zz3zz6zz9zzCzzFzzIyzLxzOvzQsyTrxXpu_osamrdl\
  pgjoPmg6p`0sT3ua9FGCJLGPP }

frm:MandelbrotMix2 {; 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==================================
;