Fractal visionaries and enthusiasts:

I rather enjoyed the half-and-half view of Seahorse Valley that I posted as the FOTD for yesterday.  Today I decided to take it one step further and see what would happen if I calculated the same type of view of North Valley.  The result is today's image.

The image closely resembles yesterday's, with the outer shape being the familiar Julia set of the area, with the bloated Mandelbrot-valley aspect filling the inside.

At first glance, today's image appears to have origin symmetry.  A second glance however reveals that it has no symmetry.

An even greater change is in the periodicity.  In yesterday's image the blunt spirals had two arms; in today's image there are three arms in each spiral.

I re-used the same color palette to bring out the similarities in the images.  But this makes today's image too much of a repeat for an honest rating.  I let it go with no rating.  The name "Order-Three Nonsense" refers to the periodicity of the area of the Julibrot pictured in the image.

The calculation time of 46 seconds is just about what the image is worth.

The most convenient way to view the Julia-Mandelbrot nonsense is to view the finished image on the FOTD web site at:

       http://www.Nahee.com/FOTD/

Heavy clouds, steady rain, and a temperature of 46F +8C spoiled outdoor plans here at Fractal Central on Thursday.  Luckily, with no outdoor plans, the fractal cats were satisfied indoors, lying by the heat.

My day was tranquil enough, which means enough work to keep my thoughts reasonably free of politics, philosophy and personal opinions in general.

Now that gardening season has ended, FL found herself with more spare time than she knew what to do with, but a latin soap-opera soon filled the empty time.  (I wish I understood Spanish.)

The next FOTD, even higher-order nonsense, will be posted in 24 hours.  Until then, take care, and will there ever come a day when someone discovers the last fractal?

Jim Muth
jamth@mindspring.com


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

OrderThreeNonsense { ; time=0:00:46.52-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=1 symmetry=none
  center-mag=-0.0201592/-0.0270368/0.9861933/1/58.5/0
  params=87/0/87/58.7/-0.125/0.66/0/0 float=y
  maxiter=2700 inside=0 logmap=yes periodicity=6
  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 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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