Fractal visionaries and enthusiasts:  

Today's scene in the East Valley area of the Z^2+C Julibrot was created by the 'ranges' feature of Fractint, a feature that I very rarely use.  It is such a rarely used feature that I am not even sure the more current Fractint-emulating programs have the ability to reproduce it.  As far as I know, the 'ranges' feature can be accessed only through a command-line entry.  The 'ranges' instructions, which are rather complicated, are available in the program documentation.

The image slices the Julibrot in an orientation halfway between the Elliptic and Rectangular.  The vaguely elephant-shaped open area in the foreground shows that we are roaming the East Valley area.  The brilliantly blue bars in the background show that regardless of where the points in the Mandelbrot set begin their journeys, if they do not escape first, they will eventually settle into the same orbits as points that begin at 0,0.  And if we look closely, we can actually see the dull red, low iteration foreground stuff gradually merging into the high iteration stuff making up the horizontal blue bars in the background.

There is no problem with the colors section of the parameter file.  Since the final 242 color registers are all solid black, I have combined them into a single register to save space.

I named the image "The Fourth Dimension".  After all, the Julibrot certainly does exist in four spatial dimensions.  The art earns a rating of an acceptable 6, while the math, which involves four dimensions, rates an improved 7.

The calculation time of 1-2/3 minutes is fast enough to keep impatience under control and slow enough to give time to watch the scene unfold on the screen.  But calculation is still a chore, and this chore may be avoided by checking the finished image on the web sites.

Clouds and rain made today a day to be forgotten here at Fractal Central.  The temperature of 48F +9C did nothing at all to help make the day more pleasant.  The fractal cats, who are now getting hard to tell apart, spent a little time sulking about the poor weather, but a lot of time working off their dissatisfaction tussling with each other.  The humans spent the day pondering the world's human problems.  The next FOTD will likely be posted in 24 hours.  Until then, take care, and one person can hardly worry about every over-hyped problem on earth.

Jim Muth
jimmuth@earthlink.net


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

TheFourthDimension { ; time=0:01:40.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=slicejulibrot4 passes=t float=y
  center-mag=+0.00204706073105023/+0.004429358557815\
  21/109.0324/3.3256/-88.4965877662025093/32.6921823\
  891347145 params=90/90/0/45/0.30025/-0.02526/0.765\
  /-0.567/2/0 maxiter=18000 inside=0 periodicity=6
  ranges=0/-1/425/500/600/800/1100/1500/2200/3300/60\
  00/18000 sound=off colors=000C00XKKKmzPqzUuzZwzcwz\
  hwzmzzzzzzzz000<242>000 }

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