Fractal visionaries and enthusiasts:

While viewing today's image, which is the last time we'll see this particular Seahorse Valley minibrot, I started wondering exactly what a minibrot is.   In the Mandelbrot set, minibrots appear as miniature Mandelbrot sets.   But at the same time minibrots extend beyond the Mandelbrot set in 2 perpendicular Julia directions, making it more appropriate when discussing minibrot rotation to consider minibrots as four-dimensional 'minibrot complexes'.

The elements in these complexes are very large in the Z-plane directions and small in the C-plane directions.   The complexes are open inside and extend throughout the Julibrot figure, appearing here and there until they are ultimately completely cut off by lower-iteration stuff.   The great difference in the C and Z dimensions of the minibrot complexes also explains the extreme stretching that so often appears in the odd-plane directions.

Today's image is another view of the past two days' minibrot complex, this time sliced in a direction rotated about halfway between the Oblate and Rectangular directions.   Conveniently, it has X-axis symmetry, which not only gives a more pleasing appearance, but also cuts the calculation time in half.   I had to stretch the image quite a bit in the horizontal direction to make it clear.

Unfortunately, I could not rate the image at a 9, as Paul wondered, since this is the third consecutive trip to the same minibrot complex.   But the rating of a 6 is still a bit above average and makes the 5 minutes required to run the parameter file just barely worth the effort.

Perhaps the best way to view the image is to surf out to the FOTD web site atbut try not to fall into the 4th dimension on the way.   If you got turned around there, you would come back as anti-matter and destroy half the continent when you self-annihilate.

The fractal cats enjoyed the typical early summer weather that prevailed here at Fractal Central on Monday.   The temperature of 86F 30C and the humidity did not bother them at all, but I decided it was time to get the energy-saving fan out of the closet and stir up a breeze or two.

The next FOTD will be posted in 24 hours.   It will not be just another view of the same minibrot.   Until then, take care, and would it be possible for a universe to exist with no conscious observers to observe it?


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

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

Seahorse_Valley-09  { ; time=0:05:12.20-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=SliceJulibrot4 float=y passes=t inside=0
  params=42.6/90/0/90/-0.7499841692570846/0.014446532\
  0644315/0/0/2/0 symmetry=xaxis mathtolerance=0.05/1
  center-mag=0/0/108000/50000000/0 periodicity=10
  logmap=2000 maxiter=16000
  colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\
  HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\
  p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\
  XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\
  gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\
  dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\
  8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\
  `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\
  Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\
  SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\
  vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\
  NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\
  4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\
  F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\
  zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrot4   {; draws most 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(p5)+c
  |z| <= 9 }

END PARAMETER FILE=========================================