Fractal visionaries and enthusiasts:

In my fractal explorations I constantly find interesting and unexpected slices of the Julibrot.  Usually I discard these almost as soon as I find them, but now I have decided to make November the month of unexpected slices of the Z^2+C Julibrot, which is the abstract four-dimensional monster that holds the Mandelbrot set as well as all the perturbed Mandelbrot sets and all the Julia sets.  Yesterday's image was the first of these slices.

At first glance, today's image appears to be a Julia set of Seahorse Valley.  But it is not.  Seahorse Valley Julia sets have either XY-axis symmetry or origin symmetry.  The mini-thing in today's scene has X-axis symmetry, something that is impossible for a Julia set to have.  The reason is that it is not a mini-Julia set, it is an Oblate set corresponding to the Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set.

The scene of the image is off to the side of the valley in the real(Z) direction at a distance of 0.5477.  The entire image has been stretched about 2-3/4 times in the horizontal direction to bring it into what is considered normal relative dimensions.  The brilliant line through the center of the image is actually the narrow space between an extension in the real(Z) direction of the two branches of Seahorse Valley of the large minibrot on the main spike of the M-set

I put more coloring effort into the image than it deserves, but the effort raises the worth a full point from 6 to 7.  The name "An Undefined Mini" means that, as far as I know, there is no generally accepted name for the type of object that appears in today's image.  So maybe I'll invent a name.

The calculation time of 2 minutes is about what the image is worth.  A bargain may be found on the FOTD web site at:

       http://www.Nahee.com/FOTD/

where the finished image is posted for near-instant viewing, and if not total, then at least partial satisfaction.

The air remained chilly here at Fractal Central on Monday, with a high temperature of only 46F +8C, but the sky was clear and the sun shone strong on the fractal cats' window shelf most all day, keeping them happy as two bedbugs in a flophouse mattress.  My day was about average.

The next FOTD will be another unexpected slice of the Z^2+C Julibrot.  It will be posted in 24 hours, give or take a few.  Until then, take care, and our world might be a better place without religion, but what would we replace it with?

Jim Muth
jamth@mindspring.com


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

An_Undefined_Mini  { ; time=0:02:12.52-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 center-mag=-0.\
  00030581/0/269/2.763 params=0/0/90/0/-1.7685291540\
  2387/0/0.5477/0/2/0 float=y maxiter=120000
  inside=255 logmap=12 symmetry=xaxis periodicity=6
  colors=0007Wb7Wc7Vc7Vc7Vc7Ud7Ud7Ud7Ud9VeAVeBVfCWfE\
  WgFWgGWhHXhIXiKXiLYjMYjNYjOYkQZkRZlSZlT_mU_mW_nX_n\
  Y`oZ`o_`paapbapcaqdbqecrgdrhesifsjgtkhtmiunjuokvpl\
  vqmvrmsrmprmnrmkrmirlfrkdsjasiZshXsgUsfSsePseNseKt\
  eHteFteCueAve7we5xe2ye0zd0yd0xc0wc0vb0ub0ta0sa0r`0\
  q`0p_0o_0nZ0mZ0lY0kY0jX0iX0iW0hW0gV0fV0eU0dU0cT0bT\
  0bS0aS0aS0`R0_R0_Q0_Q0ZP0_P0ZO0ZO0ZN0ZN0YM0ZM0YL0X\
  L0XK0WK0UK0TK0TJ0RJ0RI0QI0QH0PH0PG0OG0NG0OF0NE0NE0\
  MD0LD0LC0KC0JB0JB0IA0HA0H90G90F80F80E70E70E60E60E5\
  0E50E40E40F30F30F20E20D10C10B00A00A03A06A09A0CA0DA\
  0EA0EB4HC8KDCMEGOFKRGOTHSVIWYJ__KcaLgYNgVPgSRgPTgM\
  VfJXfGZfD`fAaf7`eN`db`cq_boZbmYblXbjWbhVbgUbeTacSa\
  bRa`QaZRaYSaWTaUUaTV`RW`PX`OY`MZ`K_`J``Ha_Fb_Ec_Ce\
  _Ag_9i_7k_5m_4oZ5qZ5sY5uY6wX6xX6yW6zW7yV7xV7wU7wU8\
  wT8wT8wT8wV7wW7wX7wZ7w_6w`6wa6wc6wd5we5xf5xh5xi5yj\
  4yl4ym4zn4zo3zq3zr3zs3zt3 }

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