Fractal visionaries and enthusiasts:

The Saturday FOTD is once again late; the reason is that FL and I again went out on a Saturday expedition, and when we returned, too little time remained in the day for a proper FOTD search.

Today's image for the 28th was found with very little searching, and shows a minibrot in the East Valley area of the Mandelbrot set.  Minibrots in East Valley of the M-set are nothing unusual, so why did I name today's image "The Fractal Victim"?  Feeling nasty, I plan on doing some not very nice things to the central minibrot in the next few days.

The image features tendril arms that are unusually long and slender, and also straighter than usually seen.  The straightness will emphasize the distortion that appears as we view the minibrot from odd angles.

Mandelbrot minibrots are not mere flat 2-D shadows.  In the 4-D Julibrot they are full four-dimensional spaces with two compact dimensions and two dimensions that appear to extend to infinity. More correctly, they *would* extend to infinity if they were not cut off by lower iteration stuff.

The compact dimensions define the Mandelbrot orientation; the potentially infinite dimensions define the Julia orientation.  The oblique angles combine both the Mandelbrot and Julia dimensions and are therefore subject to severe stretching.

I gave the image no rating, since it merely shows the scene that will be distorted in the upcoming FOTD's.  The coloring was designed to keep the corresponding parts easily identifiable when the viewing angle changes.

Unlike the calculation time of the recent elephant series, the calculation time of this series of images will be in the one-minute range, which should keep boredom at bay and everyone feeling peaceful.

Thickening clouds and an un-springlike temperature of 48F +9C made today (Saturday the 28th) a day to be forgotten here at Fractal Central.  The fractal cats forgot the day even before it began.  The humans, out on an expedition, took things in stride.  The next FOTD will be posted in 24 hours.  Until then, take care, and with cameras everywhere and the alien space ships supposedly navigating in our skies, why are there no clear pictures of UFO's?

Jim Muth
jimmuth@earthlink.net


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

The_Fractal_Victim { ; time=0:01:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/\
  1.392609e+007/1/90/0 params=0/0/0/0/0.266251413921\
  /0.0034281189961/0/0/2/0 float=y maxiter=1500
  inside=0 logmap=152 periodicity=6
  colors=000cYUbXUaWU`VU_UUZTUYSUXRUWQUVPUUOUTNUSMSR\
  LSQKSPKQOKONKMMKKLKILKGLLHLMIKNIKPJKRKKTKMVLOXMPZM\
  R`NTaOVbOWcPXdPYdSYdVYdYYd`YdcZcgZdiZdlZeoZer_eu_e\
  x_dw_bv_`u`YtaVobSjcPedM`dJWeFRfCMg9Hh6Ci37h03f14c\
  24`24Y34V34S44P54M54J64G64D94AB47D44F41H42K62N72R9\
  2UA3VD4UG5SJ6QL7OO8NR9LTAJWBHZCF`DEcECfFAhG8kH6nH5\
  pJ8nLBmNElPGkRJjTMiVPhWRgZOi`MjcKleHmhFnjDpmBqo8rr\
  6tt4uv2vq3tm3ri4qe4oa5mX5lT6jP6hL7gH7eD7dJCfOGhTLi\
  ZPkcUmhYniVljTjkQikOglLemJdnGbnE`oB_p9Yq6Wq4Vp5Uo5\
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  BehCghCiiCliDnjDpjDskEukEwkEyjFriFlhFegF_fFUeFNdFH\
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  LQJKTNJWSHZWGa`FddDgiCjmBceCXZCQSDJKDCDE56ENJRdWch\
  aSkfGgiEdkDamCZoBVqASs9Pu8Mw7Jz6PzFUzOZzWczdhzldzi\
  azfzzczz`zzYzzVzzSzzQzzSzzTzzUzzWzzXzzYzzZzzWzzUzz\
  SzzQzzOzzMzzKzzIzzFzzDzzB }

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