Fractal visionaries and enthusiasts:

Today's image gets no rating.  Why?  Because it's a virtual repeat of yesterday's image.  The difference is that, while yesterday's image was sliced in the Oblate direction, today's is sliced in the Rectangular direction, which consists of the imag(Z) and imag(C) axes of the Julibrot.

IMO, what made yesterday's scene so curious is the fact that the fractal terminates on the left and right at values of plus and minus 1.618...., (the golden ratio), while the large valleys meet at plus and minus 0.618...., the reciprocal of the golden ratio).

This is curious enough, but when I checked the horizontal terminal points of today's image, I found a value of plus and minus 0.78615....  What an incredible coincidence it is that this is the reciprocal of the square root of the golden ratio.  (The two large valleys in today's image meet at plus and minus 0.521555...., though I have yet to find anything significant in this value.)

Mathematical interest aside, today's image is simply a variation on yesterday's image, with the same color palette.  Those who enjoyed yesterday's will enjoy today's almost as much.  Those who thought yesterday's image was boring will be no more impressed by today's.

The name "Curious Coincidence" refers to the mathematical aspect of the image.

The calculation time of only 3 seconds is mercifully brief.

Wednesday began with clouds here at Fractal Central.  But the clouds broke up by midday, leading to a sunny afternoon with a temperature of 72F 22C.  These conditions were perfect for the fractal cats, who spent several hours in the sun that streamed in the southwest window.  My day was average; FL had a similar day.  The next FOTD will be posted in 24 hours, and is likely to be another mathematical curiositiy, though one with far more artistic impact.  Until then, take care, and why does the number epsilon equal minus one when it is raised to the power of imag(PI)?

Jim Muth
jamth@mindspring.com


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

CuriousCoincidence { ; time=0:00:03.35-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/1.398/1/\
  90/0 params=90/0/0/90/-1/0/0/0/2/0 float=y inside=0
  maxiter=300 inside=0 outside=real periodicity=6
  colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\
  HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\
  vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\
  OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\
  zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrot4   {; 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=========================================