Fractal visionaries and enthusiasts:

The classic Mandelbrot set might be the greatest of all fractals, but let's not forget the Z^3+C Mandeloid, the cubic figure, which is almost as great and in addition holds some features with no analog in the classic set.

To be honest, the parent fractal of today's image is not exactly the Z^3+C Mandeloid.  It is the Z^(3.003)+C Mandeloid.  The differences are very small however, and I'm sure that a virtually identical scene could be found in the pure Z^3 set.

I stumbled upon the scene by accident while searching for rectangles in the Julia sets.  Instead of rectangles, I found today's image, a fair consolation prize.

When all the pluses and minuses were figured in, I gave the image a rating of a 7.  The name "Cubic Action" needs no explanation.

A heavy gray overcast and temperature of 66F 19C muffled things here at Fractal Central on Friday the 13th.  The fractal cats, not believing in bad luck, took things in stride, and worked off their excess energy chasing each other up and down the hallway.

The humans had another un-notable day, where everything went along pretty much according to schedule.  The next FOTD will be posted in 24 hours.  As always, if an antiquing expedition comes up on Saturday, the next FOTD might be late.  Until next time, take care, and if the solutions to the world's problems are as simple as some people say, why haven't the problems been solved?

Jim Muth
jamth@mindspring.com


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

Cubic_Action       { ; time=0:03:31.19-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1
  center-mag=-1.096032374971432/-0.000000000036281\
  81/6.781329e+011 params=0/0/0/90/0/0/0/0/3.003/0
  float=y maxiter=2700 inside=0 logmap=428
  periodicity=6 mathtolerance=0.05/1
  colors=00090`80a70a90_A0ZC0YD0XF0WG0VI0UJ0TL0SM0RN\
  0QO0PO0PP0PP0OP0OQ0OQ0OQ0NR0NR0NR0NO0QL0SI0UF0WC0Y\
  90_C0bF0dI0gL0iO0lR0nU0qX0s_0vb0xc0sc0na0j`0d_0__0\
  U_0OZ0RX0UU0XR0_O0`K0bG0dC0f80g90i50k10m30n60lD0jF\
  0hH0fJ0dL0cN0cP0bQ0aR0_S0YT0WV0UX0SV0QT0OR0MP0KN0K\
  L0KK0KI0KG0KF0KF0KC0KB0KA0KC5PDAUEFZEKcFPhGUmHSlHR\
  kIPjJNiKLhKJgLHfMFeNDdNCcRLXVTQZaKbiDfq7bkD_fIW`OT\
  WTQRYRU_RW`RYaR_bRacRcdSefSggSihSkiSmjSokSqlQniPlf\
  OjdNhaMfZLdXKbUI_RHYPGWMFUJESHDQECOCEQEFSGHTIIVKJW\
  MLYOMZQO`SPaUQcWSdYTf_UgaSibQjbPlcNmcModKpdIqdHseF\
  teEvfCwfBxfUmiccchhhmmmooorrrtttwwwvwzuuuptpnormqn\
  jnkgkhdgeadb_a_TXWMSTFOQHWWJcaLkfOlcQlaTlZVmXXmV_m\
  SamQcnOfnLhnJjnHhkFghEffCdcBc`9bZ8c`7da7db7ec6ed6f\
  e6ff5gg5gh5hi4hj4ik4il4hm8gmBfmzemzdmzcmzbmzanz`nz\
  _nzZnzYnzXnzWnzVzzUzzUzzTzzmzzmzzmzzmzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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