FOTD 30-08-10 (Total Abstraction [6])

30 Aug 2010

      FOTD -- August 30, 2010 (Rating 6)

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.

This abstract stuff becomes quite clear when the image is seen.  
It may be seen on the FOTD web site in finished form at:

       <http://www.Nahee.com/FOTD/>

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

Jim Muth

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