Fractal visionaries and enthusiasts:  

The artistic rating of today's image is a 9.  This might be a bit of an exaggeration, but the math rating of 9-1/2 is definitely well-earned.  Who ever heard of an escape-time fractal with an exponent of Z as close to unity as 1.0009, the value that creates the parent Julibrot that holds today's scene? True, some hyperdimensional trickery was necessary to reveal the details, but the image does exist, and that is that.

When the parent fractal is calculated with a reasonable maxiter of around 1000, the parent fractal is little more than a lopsided and featureless empty circle.  But when the maxiter is increased to 48000, the parent takes on the vague shape of the Mandelbrot set.  Today's scene lies in what would be the East Valley of this wannabe Mandelbrot parent.

The name "The Great Paradox" refers to the surprising detail in the image.  The puzzle might not equal the so-called 'measurement problem' of quantum theory, but to me at least, the detail in today's image was totally unexpected.

Unfortunately, there is a price to pay for the surprise.  With such a large maxiter and a rather complex formula, the image takes almost an hour to finish.  The web sites can eliminate the wait however.

Typical blustery autumn weather prevailed here at Fractal Central today, with blustery winds, dark scudding clouds, and a temperature of 50F 10C.  Both the fractal cats and humans had too much to do to complain about the less-than-ideal weather.

The next FOTD will be posted in about two days.  Until whenever, take care, and prepare!  The end of the world is *NOT* nigh!

Jim Muth
jimmuth@earthlink.net


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

The_Great_Paradox  { ; time=0:52:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=1
  center-mag=2.11546/0/11.9/1.652/-90/0
  params=45/0/45/0/1.5/0/0/0/1.0009/0 float=y
  maxiter=48000 inside=0 logmap=-3188 periodicity=0
  colors=000HKNKMNNNNPONQPORQOSROTSOTTOUUPVVPWWPXXPX\
  YPYZPZ_Q_`Q_aQ`bQacQbdQceRcfRdgRehRfiRfiRdiSchTagU\
  `fUZeVYdWWcWVbXTaYS`ZQ`ZP__NZ`MY`KXaJWbHVcGUcITdKS\
  ePSeUWdZ_dcbchfcmjbroivtqvzzvtqrqfmnYhiRecOc_MaXJ_\
  THXPEVMBTK9RH6PF4ND6KB8I9AG7CE4ED0GC0IB0KA0LA0NUIz\
  UIzUIzVIzVHzWGzWFzWFzM2zJ1zG1zD0zA0z80z95z99z9Ez9I\
  z9Mz9Rz9Vz9Zz9cz9gz9kzBhzCfzEdzFbzG`zI_zJYzKWzMUzN\
  TzORzQPzRNzSMzUKzVIzWGzYFzZDz_Bz`AzaCzbEzcGzdIzeKz\
  fMzfNzdOzcOzbOzaOz`Pz_PzZPzYPzXPzWQzVQzUQzSQzRQzQR\
  zPRzORzNRzMRzLSzKSzJSzISzHSzLUzOWzRYzU_zYaz`czcezf\
  gziizjjzkjzkjzljzljzmjzmjznjzojzojzpUzpUzqUzqUzrUz\
  sUzsUztUztUzuUzuUzvUzvUzlUzbUzTezUbzV`zWYzWWzXUzYR\
  zZPzZNz_Kz`IzaFzaDzbBzc8zd6zd4ze6zf8zg9zhBziDzjEzk\
  GzlIzmJznLzoNzpOzqQzrSzsTztVztWzrXzpXznXzmYzkYziYz\
  gYzfZzdZzbZzaZz_azXczUfzShzQjzOkzMlzKmzInzGpzEqzSt\
  zJvzAxz1zz4uz7pz9kzCfzFbz }

frm:SliceJulibrot5   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=(-z)^(real(p5))+c
  |z|< esc }

END PARAMETER FILE=========================================