[Fractint] FOTD 03-05-03 (The May Parent [NA])

3 May 2003

      FOTD -- May 03, 2003 (Rating NA)

Fractal visionaries and enthusiasts:

The Mandelbrot set is sometimes called the most complex object 
in the world of mathematics.  And it truly is a complex object.  
But there are other fractal objects created by other fractal 
formulae, which are more complex than even the M-set.  Of 
course, since the M-set is infinitely complex, these other 
objects would appear to demand a higher order of infinity.

Today's image could be one of these 'higher' fractals.  It is 
titled "The May Parent".  I give it this name because, for the 
rest of the month of May, I shall use it as the source of my 
FOTD images.  This limitation in no way implies a shortage of 
images or a reduction in their quality, though on occasion I 
will go beyond my normal style of image with a midget at the 
center.

The formula mixes one negative part of Z^(-11) with ten negative 
parts of Z^(-1.1), then adds 1/C before being calculated with a 
bailout radius of 625.  In some places, the oversized resulting 
fractal is filled with holes like a swiss cheese.  In other 
places, it appears to hold the usual Mandel-stuff.  In yet other 
places, it is filled with rings, while a prominent fan-shaped 
element fills the center.  The variety is endless, and the 
fractal has midgets hiding almost everywhere.

I gave today's image no rating, since it is not really a 
finished product, but rather the source of the next 28 FOTD 
images.  The render time of a little over one-minute should give 
little difficulty, but for extra convenience, the completed GIF 
image is posted to the FOTD web sites at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The rain that was expected here at Fractal Central on Friday 
never arrived.  Instead of the rain, we had a mostly sunny day 
with a temperature of 81F 27C.  The fractal cats thoroughly 
enjoyed the unexpectedly pleasant day, and spent several hours 
romping in the yard.

Today is starting cloudy and quite a bit cooler -- once again 
threatening rain.  Will good fortune prevail, giving the fractal 
duo another good day?  Only time will tell.  My day will turn 
good when the work is finished, so until next time, take care, 
and see you in 24 hours with the next image.

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

START 20.0 PAR-FORMULA FILE================================

The_May_Parent     { ; time=0:01:11.96--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix2 function=recip passes=1
  center-mag=3.56788/-0.692098/0.1341384/1/135/-3.77\
  822773067748585e-014 params=-10/-1.1/-1/-11/0/525/\
  0/0 float=y maxiter=400 inside=0 logmap=yes
  periodicity=10 colors=000CHgEIfGJgIJgKKcLLhNMePMiR\
  NhTOjVPkXPkYQl_RlaSmcSmeTmgUmiVmjVmkTmlRmmPmmOmnQl\
  oSjpUipWgqYfr_dsacscate`ugZwiYzkUwmRroOrqLmsImuFhw\
  CFw9Au69t69t69s69s68r68r68q68q67p67p67o67o66n66n66\
  m66m65l65l65k65k64j64j64i64i64i65g75f85e96cA6bB6aC\
  7`D7ZE7YF8XG8WH8UI9UJ9UK9ULAUMAUNAUOBUPBUQBURCUSCU\
  TCUUDUVDUWDUXEUYEUZEUZCUYAUX9UY9UY9UY9UY8UZ8UZ8UZ8\
  UZ7U_7U_7U_7U_7T_FScMSfURi`RleYeidZmkTqrMuyGowMjvS\
  etY`scVqiQpoLnuGmzHmxImwJmvJmuKmtLmrMmqMmpNmoOmnOm\
  mVm8Wx9Xw9YwAYwAZwB_wB`wC`wCawDbwDcwDcwEdwEewFfwFf\
  wGgwGhwHiwHiwHgwJewKcwMawN_wOYwQWwRUwSSwUQwVOwXNwY\
  LwZJw`HwaFwbDwdBwe9wg7wh5wi3wk1wl0wm6whBwcGwZLwURw\
  PWwK`wFewAjw5mw6ow7qw8sw8uw9wwAywAvwFtwJqwOowSmwXj\
  w`hweewicwnawrIw8NwBRwEVwGZwJcwLgwOkwQowTswVtwUuwU\
  vwUvwUrwWnwYkw_gw`dwb`wdYwfUwgQwiNwkJwmGwnCwp9wr5w\
  t2wu8whEwWKwJPw7Ow9OwAOwBOwCOwDOwFOwGNwH }

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 20.0 PAR-FORMULA FILE==================================

[Fractint] FOTD 03-05-03 (The May Parent [NA])

Jim M.