Fractal visionaries and enthusiasts:

Usually, I put little effort into fractal spirals.  They're very easy to find and nearly everyone does them.  But the spiral in today's image is so unusual that I had to make it a Fractal of the Day.

I found the spiral when I tried to extend the trick of the two most recent FOTD's to the valley of the period-10 bud on the northeast shore line of the Mandelbrot set.  The trick worked as I thought, producing the anticipated image, but I never expected the image to be filled with such hairline-thin spirals.

Today's scene is a blow-up of a small part of the full image, which in itself is quite interesting.  (The full image will be the FOTD for tomorrow, November 07.)

Actually, images with very fine details such as today's and tomorrow's are improved by anti-aliasing, which helps eliminate the awkward breaks in the finer parts.  Because of the fine detail in today's image, I recommend calculating it at the highest resolution available.

The name "Almighty Spiral" is overblown.  The spiral is not all that great when compared to some that have been found by others, though it is probably the best I have found.

If spirals were not so commonplace, I might have rated the image higher.  As it is, a rating of a humdrum 6 will have to do.

The calculation time of 11 minutes is for a resolution of 640x480.  It will be far longer if the image is rendered at a higher resolution than this.  But for the true fractal-spiral fan, the result will be worth the wait.

The finished image is posted on the FOTD web site at:

       http://www.Nahee.com/FOTD/

Sprinkles of rain fell during the morning Friday here at Fractal Central.  A few breaks of sun appeared during the afternoon, but not enough to lure the fractal cats to their shelf by the southwest window.  The temperature of 52F 11C was about normal for early November.

The next FOTD will be posted in 24 hours.  Only a surprise antiquing trip could delay it.  Until next time, take care, and expect the unexpected.

Jim Muth
jamth@mindspring.com


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

Almighty_Spiral    { ; time=0:11:12.40-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=t periodicity=6
  center-mag=-0.448511/-0.894674/9.159484/1/114/0
  params=89.96/0/89.96/0/0.3272613/0.0561252/0/0
  float=y maxiter=15000 inside=0 logmap=-3
  colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
  OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\
  EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\
  H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\
  dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\
  rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\
  GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\
  _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\
  LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\
  Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\
  TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\
  5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\
  zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\
  wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\
  rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
  zrwzrwzrwzrwzrwzrwzrwzrwz }

frm:SliceJulibrot2   {; draws most 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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