Fractal visionaries and enthusiasts:

Today's image is a scene in the Rectangular (imag(c),imag(z)), orientation of the Z^2+C Julibrot.  The scene is located near the -1.416 point of the main spike of the Mandelbrot set.

The rating of a 6 is a come-down from the lofty ratings of the past several days, but the image is still worth a look, and the calculation time of just over 2-1/4 minutes will cause little inconvenience.

The name "Total Abstraction" refers to the nature of the four-dimensional Julibrot figure, as well as all other 4-D things.  The curious thing about this is that when one or two dimensions of the total abstraction are discarded by taking slices, the slices prove to be very real.

The sky was once again cloudless here at Fractal Central on Sunday, but the temperature of 90F 32C was a bit too warm for human or cat comfort.  The fractal cats took up residence on the cool kitchen floor, while the humans took it easy on the porch.

The next FOTD will be posted in 24 hours.  Until then, take care, and as I see it, the concept of meaning is an invention of intelligent minds.  Since the universe apparently has no mind, how then can it have a meaning apart from what we give it?  But at the same time, what is the evolutionary advantage of this human tendency to waste mental energy searching for meaning and even to invent meaning where none exists?

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

Total_Abstraction  { ; time=0:02:15.37-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1
  center-mag=0/-0.028319668443599/3349.992/4.7924/180
  params=90/0/0/90/-1.41665335/0/0/0/2/0 float=y
  maxiter=5000 inside=0 periodicity=6
  colors=000UQwUQwUQwUPwTPwTPxTOxSOxSOxSNxSNyRNyRMyR\
  MyRMyQLwPKuOKtOJrNJpMIoMHmLHkKGjJGhJFgIFeHEcHDbGD`\
  FCZECYEBWDBVCAT000C9RB9QA8O98M97L86J76H75G65E54D44\
  B439328226214113001JMxILvIKtHKsHJqGJpGInFImFHkEHjE\
  GhDFgDFeBDbBD`BC`BCZACYACW9BW9BU9AS89R89P78O79M6AL\
  6BJ5CI5EG4HF4KD3PC3UA2Z92c71h61m40r30v1Az6Kx5Pv4Ut\
  3Zr2cp1hn8ml7rj7vh7zf6vd6rc6ma6h_5cY5ZW5UU4ST4QR4O\
  P4MN3KL3IK3GI2EG2CE2AC28A1691471250130010L1xK0wK0v\
  K0uK0uJ0tJ0sJ0sJ0rI0qI0pI0pI0oH0nH0nH0mH0lG0lG0kG0\
  jG0iF0iF0hF0gF0gE0fE0eE0eE0dE0cD0bD0bD0aD0`C0`C0_C\
  0ZC0ZB0YB0XB0WB0WA0VA0UA0UA0T90S90S90R90Q80P80P80O\
  80N70N70M70L70L70KA5JFAIKFJPKKUPPZUUcZZhccmhhrmmvr\
  rzvvuzzszzqzzozzmzzkzzizzgzzezzcyzbxzawz`vz_uzZtzY\
  szXrzWqzVpyVoxUnwUnvTmuTluTltSksSjrRiqRipQhpQgoQgn\
  PfmPelOdkOdkOcjNbiNbhMagM`fL_fL_eLZdKYcKYbJXaJWaIV\
  `IV_IUZHTYHTXGSXGRWGRVFQU }

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