Fractal visionaries and enthusiasts:

It's a new month and time for a new theme.  To escape the rut of mathematical interest only, I have decided to make May the month of images with artistic value.  And there is no formula I know of that creates images more artistic than those created by the workhorse MandAutoCritInZ.

To lead off the month, we check the parent fractal that results when Z^(2.01) is subtracted from Z^2 and straight C is added on each iteration.  Intuition says that this fractal will be little more than an oversized Mandelbrot set.  Well, the fractal is oversized sure enough.  A bailout radius of 1100 was neded to fit it all in, but the fractal is far from an everyday Mandelbrot set.

This parent fractal actually resembles a Z^(2.5)+C Mandeloid far more than it resembles the classic M-set.  In addition, it is rotated 180 degrees so that the side normally on the east lies on the west.  Its East Valley has split into two well-defined valleys, with the area between filled with many discontinuities that call for exploration.  Its main period-2 bud has sprouted two large sub-buds, each growing its own infinitely divided main spike.  Today's image is located in the area of discontinuities between the two large sub-buds.

The name "Testing 1-2-3" is what a sound man traditionally says to test the levels of his sound system.  It came about when I saw myself setting up for an actual entire month of worthwhile fractals.  The rating of a 7 that I gave today's image is not particularly outstanding, but I'm still not totally back into artistic mode.  The ratings will (hopefully) increase as the month progresses.

The calculation time of 1-2/3 minutes is a fair price for a fractal with a rating of a 7.  And the web sites are always there for those who would rather miss the fun of calculation.

Today brought a mix of clouds and sun to Fractal Central.  The pleasant temperature of 77F 25C made the periods of clouds seem much more pleasant than they might have been.  The fractal cat duo was very active, chasing each other up and down the hallway until Nicholas finally ran out of energy.

The humans, who never chase each other up and down the hallway, had a more restful day doing routine things.  The next FOTD will be posted soon.  (I'll no longer mention 24 hours, since the time between postings is irregular, and has rarely if ever been exactly 24 hours.)  Until next time, take care, and it looks like it might be fractals all the way down.

Jim Muth
jimmuth@earthlink.net


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

Testing_1-2-3      { ; time=0:01:40.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident float=y
  center-mag=+21.50591668895752/-0.1715777757829369/\
  3.11306e+009/1/82.5/0 params=1/2/-1/2.01/1/1000/0/0
  maxiter=1250 inside=0 logmap=114 periodicity=6
  colors=000u7fr6eo7dlGZiSUdZOZdJTiDOm8No6Mm7Lj7Jf6I\
  c6G_5FW5DS4CO4AK39G37E26B0590460340220000FpaEm_EkY\
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  Z3eX3cW3aU3ZS3XR3VP2SN2QM2OK2MI2JH2HF2FD2CC2AA2882\
  0sz1pw1nt1lq2in2gk2eh2be3`b3Z_3WX4UV4SS4PP4NM5LJ5I\
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  3mP3mN3mU3mU2mU2mU2mU2mU2mU2mU2mUmmUmmUmmcmmcmmcmm\
  cmmcmmcmmcmmcmmcmmcmmcmmcmmcmzm6zm6zm5zm5zm5zm4zm4\
  zm3zm3zm2zm2zmfzmczmazm_zmXzKzzJzzIzzHzzGzzFzzEzzD\
  zzCzzBzzAzz9zz8zz_zzXzzVz }

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