Fractal visionaries and enthusiasts:

Rarely does a parent fractal become Fractal of the Day, but today is the second consecutive day on which a parent fractal has been featured.

In yesterday's image we saw that the (-Z)^(1.05)+C Julibrot apparently holds no interesting semi-chaos, at least not in the area of Seahorse Valley.  In today's image we find that first impressions are sometimes wrong.

Today, we check the hump that passes for East Valley in the Mandelbrot aspect of the Julibrot.  We check it at an angle double rotated 37.5 degrees toward the Julia direction, and what we find is total chaos.  While all the edges in yesterday's image were smooth, today's image shows nothing but chaos in its eastern parts.  To add to the interest, this chaos consists of discontinuities, which vary widely in character in different parts of the image, yet have a similar theme in restricted areas.

Such a mixed-up Julibrot surely has many additional curious slices in this East Valley area.  I'll be checking other slices over the next few days, and I would not be surprised if some slices achieved FOTD image status.

The name "The Big Surprise" expresses my feelings when I checked the 37.5,37.5 angle of today's slice through 'east hump'.  The rating of a question mark shows my indecision.  The mathematical interest is certainly there, and would rate about an 8, but take this math interest away and the artistic value falls short of FOTD reference standard.

The redeeming feature is the super-fast calculation time of 50 seconds, which will give no one a reason to regret the wasted time if the image falls flat with them.

Conditions were windy here at Fractal Central today.  The gusts near 50mph, 80kph kept the leaves swirling.  Otherwise the partly cloudy skies and temperature of 64F 18C were harmless.  The fractal cats were also pretty harmless, sleeping as they did through a good part of the afternoon.

FL and I stopped by a local 'occupy' demonstration around noon.  Somehow I found myself holding a we're-not-going-to-take-it-any-longer sign and getting honked at by passing cars.  Luckily, no harm was done to my middle-of-the-road political reputation, since all sides apparently agree on the same problem, if not the solution.  We then spent the rest of the day on a short antiquing expedition.  The next FOTD will be posted in 24 hours.  Until then, take care, and when the time is right, the answers will become obvious.

Jim Muth
jimmuth@earthlink.net


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

The_Big_Surprise   { ; time=0:00:50.15-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 center-mag=1.07545/0/\
  0.3427852 params=37.5/0/37.5/0/1.1513/0/0/0/1.05/0
  float=y maxiter=15000 inside=0 logmap=yes
  symmetry=xaxis periodicity=9
  colors=000blYcmXdnXdoWeqWfrVfsUgtUhvThuSixSjwRjzRh\
  vQgwQfuQetPdtPcqPbrOaoO`oO_lNZmNXiNWjMVfMUgMTdLSdL\
  RaLQbKP`KO_KNZJLXJKWJJUIITIHSIGQHFPHEOHDNGCLG8NHBL\
  GDNGGNGIPGLSGNUGQXGSZGU`GT_FTZFTYFTYFTXETWETVESVES\
  UESTDSTDSSDSRDSQDRQCRPCROCRNCRNCRMBRLBRLBQKBQJBQIA\
  QIAQHAQGAQFAPF9PE9PD9PD9PC9PB8PA8OA8O98O88O77O77O6\
  7O57O57P68Q69R7AS7BS8CT8DU8DV9EW9FWAGXAHYBIZBJ_BJ_\
  CK`CLaDMbDNcEOcEPdEPeFQfFRgGSgGThHUiHVjHVkIWkIYlJ_\
  mIanGcoEeqCgrAis8ku6mv4ox2qz0sy1ux2ww2ww3ww3ww4ww4\
  ww5ww5ww6ww6ww7uw8sw8qw9ow9mwAkwAiwBgwBewCewCewDew\
  EfwEgwFgwFhwGhwGiwHiwHjwIkwIkwJlwKluKmsLmqLnoMomMo\
  mNpmNpmOqmOqmPrmOsmPrmPqmPpmQomQomQnmRmmRlmRlmSkmS\
  jmSimTimThmTgmUfmUfmUemVdmVcmWczYaz_`za_zcZzeXzgWz\
  iVzkUzmTzoRzqQzsPzuOzwMzxLzzKzzJzzIzzGzzFzzEzzDzzB\
  zzAzz9zz8zz7zz5zz4zz3zz2zz1zz2zz2zzfzzezzezzdzzczz\
  czzbzzazzazz`zz`zz_zzZzzZ }

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