Fractal visionaries and enthusiasts:

Today's surreal scene is named "New Elephant View".  The name shows that it is a new view of East Valley of the Mandelbrot set, which is sometimes called Elephant Valley.

The Mandelbrot set is a two-dimensional slice through the center of the four-dimensional Julibrot figure, which results when the expression Z^2+C is iterated.  (Two complex numbers equals four variables.)

The Mandelbrot set does not slice the Julibrot figure into two separate parts however.  It simply cuts a two-dimensional hole through the Julibrot.  A three-dimensional slice would be needed to make the Julibrot fall apart.  Nor is the Z=0,0 slice the only slice of the Julibrot that produces the familiar M-set shape.  I suspect but do not know for sure that there are an infinite number of two-dimensional slices of the Julibrot that produce Mandelbrot sets.

Since the Julibrot is four-dimensional, it has six mutually perpendicular two-dimensional slices through every point.  Two of these orientations are quite familiar -- the Mandelbrot and Julia directions.  The names of the other four orientations are my own inventions -- the Oblate, Rectangular, Parabolic and Elliptic directions.  Today's scene slices the Julibrot in the Rectangular direction, thus it may properly be called a Rectangular set.

In the image, the vertical direction is the imag(z) axis, while the horizontal direction is the imag(c) axis, thus the scene is a hybrid -- 1/2 Mandelbrot and 1/2 Julia.  The slice is offset 0.5 in the real(z) direction.

With all this technical stuff and not too much image to work with, I could not give the image a rating.  Setting the inside to something like 'bof60' or 'atan' adds more detail to the scene, though I prefer the stark black background of inside=0.

The fractal cats appeared unusually happy about the nondescript conditions here at Fractal Central on Sunday, which was about as average as a day could be.  The temperature of 70F 21C was average, the partly cloudy sky was average, the northeast wind was average, and the forecast of coming rain was typical.  My day was average also.  The next FOTD will be posted in 24 hours, which is average.  But for today only, I will have no thoughtful but intentionally silly or controversial closing remark, which is most un-average.

Jim Muth
jamth@mindspring.com


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

New_Elephant_View  { ; time=0:00:49.16-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 center-mag=0/0\
  /1.1/13.5 params=90/0/0/90/0.28/0/0.5/0/2/0 float=y
  maxiter=2500 inside=0 logmap=10 periodicity=6
  colors=000kqThqVepWcnYal__jaYheWfiUeiRdhSchRaePZaO\
  PUOLPKHKHczDdzAfz6jz3kz2mz2mz2mz2nz2nz1oz1qz1sz1qz\
  1oz2nz2mz2lz2kz3jz3iS3hU3gW4fY4e_4da4cc5be5ag5`i5_\
  k1Xm5_l9alDdkHfkLijPkjTniVoiWpiOkUGfEHeDIeDJdDKdDL\
  dDMcDNcDNcDObDPbDQbDRaDSaDT`DT`DU`DV_DW_DX_DYZDZZD\
  zuDzuGzuIzuLzuNzuQzmSzmVzmXzm_zmazmdTMzTLzSKzSJzRI\
  zRHzRGzTHzzI0zJ0zK0zL0zM0zN0zN0zO0zP0dQzfRzgSzhTzi\
  QziTzcWzYYzS`zMczGezAhz8iz5jz9izCizFizIizLizPizSiz\
  VizYiz`izehzcizbjzakz`lzZmzYnzXozWpzVqzTrzSszRtzQu\
  zPvzNwzMxzLyzKzzJzzLzzMzzNzzPzrQzzRzzQzzSzzTzzUzzV\
  zzWzzXzzZzz_zz`zzazzbzzczzdzzatzZozWizTdzQZzNUzKOz\
  IJzJLzKMzLOzMPzNRzOSzPUzPVzQWzRYzSZzT`zUazVczWdzWe\
  zXgzYhzZjz_kz`mzanzZtzaozcjzfezh`zkWzmRzoNzqTzsYzu\
  czvhzslzppzmtzjxzgzzdzzczzbzzawz`tz_qzZnzYkzXhzWez\
  VbzU_zTXzSUzRRzQOzPLzPGzOIzOKzOMzOOzOPzORzOTzNVzNX\
  zNYzN_zNazNczKazNdzPgzSjz }

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