[Fractint] FOTD 17-07-07 (Uncut Jewels [7])

17 Jul 2007

      FOTD -- July 17, 2007 (Rating 7)

Fractal visionaries and enthusiasts:

In today's fractal formula we combine 1 part of Z^(1.5) with 1/2 
part of Z^3 and add straight C.  This formula produces a parent 
fractal that consists of two symmetrical and partially merged 
Mandelbrot sets facing north and south.  Today's image is 
located on the western shoreline near the X-axis, where the two 
sets merge, and a small but curious kind of bud is located.

The parent of today's image is symmetrical around the X-axis, 
but it is a very critical type of symmetry.  If the exponents of 
Z are changed from 1.5 and 3, the symmetry vanishes at once.  If 
Z^3 is changed to Z^2.5, and all else kept the same, the 
resulting parent fractal is one of the most unusual I have yet 
encountered.

I named today's image "Uncut Jewels".  The four faceted elements 
remind me of diamonds in the rough.  I rated it at a 7, which 
might be a bit high, but it's really a rather pleasing fractal.

The included parameter file runs in 31 seconds on my fast 
fractal computer.  The old P200 would take about 3 minutes to 
finish the job.  As always, the best way to see the finished 
image is to go online to the FOTD web site at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and view it instantly there.

With a temperature of 86F 30C, Monday was a bit too warm to be 
considered perfect.  But I doubt that anyone noticed the 
deficiency.  The cats kept themselves occupied chasing each 
other, hiding, and suddenly pouncing.  My day was suitably busy. 
If all goes well, tomorrow will be the same.

The next FOTD will appear in 24 hours.  Until then, take care, 
and if a farmer has seven daughters and each daughter has a 
brother, how many children does the farmer have?

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

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

Uncut_Jewels       { ; time=0:00:31.04-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=ident
  center-mag=-0.26485847107386810/-0.037316662862560\
  15/1.227384e+009/1/97.5/-7.40612221022743378e-005
  params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=750
  inside=0 logmap=64 periodicity=10
  colors=000666999DDDGGGJJJNNNQQQZZZiiilllnnn0rp0tr0\
  uz0uz3lwBelGZlJblNglQllUrlOpXOlIOiGOjGOlENlEUj9Zi5\
  eg2j`0pQ0j90b00m89nTSp_VrdVtlhuruzzzzzzNG6B8600600\
  6808S08N08E08809O0BeBJwNUzZbzjlzwuzz0zz0zzzzz0zz0z\
  rSzUOz6LzcU0z`0zX0zW0zU0zQ0zO0zN0zJ0zG5zD9z9Gz6Lz3\
  Qz2Sz0Uz0Wz0Xz0Xz0Zz0`z2`zDbzQbzbcznczzXyjSyXNwJGw\
  5Bu06u0WzwZyu`rtbircbrgWpiNnjGll9lbQuSezIwz8zzIzzS\
  zz`ztjzjtzcuziuzlwznwppycryUtzItz8uz0wz0yz0yu0zp0z\
  j0zc0zZ3zU9zNEzIJzDOz6Uz2`z0ez0jz0pz0uzNG0OL0QQ0QU\
  0SZ0Ub0Ug0Wj0Xp0Xt0Zy0Zz0Sz0Lz0Ez08z02z00z20z50z65\
  n0OS0i60z00z00z00z03z0Bz0Lz0Uz3bz5jz6tz3jz0cz0Xz0Q\
  z0Jz0Dz06z00z00z60zD0zJ0zQ0zX0zc0zj0zr0zy0zz0zz0zz\
  2zz3zz3zzDzzLzzUzzbzzlzzuzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzbzzDzz0zz0zz0zz0zz0zz0zz2zz5zz8zzBzzEzzIzzL\
  zzOzzSzzWzzQzzNzzJzzEzzBzz8zz5zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0 }

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=========================================