Fractal visionaries and enthusiasts:

I always have enjoyed elephants.  When I was young, they were my favorite animals at the circus.  Now that I'm no longer young, they are my favorite animals in the Mandelbrot set.  Of course, it doesn't take much to make elephants my favorite animals in the M-set, since the only other animals are seahorses, which are more of a curiosity.

The Mandelbrot elephants live in the valley on the east side of the M-set, which is appropriately named "Elephant Valley", or sometimes simply "East Valley".

An infinity of the ponderous pachyderms inhabit the valley, every one of them standing guard over its own particular bud.  But they guard their buds only in the Mandelbrot plane of the Julibrot.  In the other planes, the elephants forget their buds and wander off in different directions, becoming ever more distorted the farther they roam.  In today's image this distortion has become quite large.  In fact, some elephants are only partly there, which is the reason I named the image "Elephant Pieces".

Today's image is sliced in the 'Oblate' direction, which is determined by the imaginary (y) direction of the Mandelbrot planes and the real (x) direction of the Julia planes.  The slice passes through the East Valley complex of the Julibrot at point +0.28 on the X-axis of the M-set, but being centered at the point 0.5 on the imaginary Julia axis, it is far from being centered on the valley.

I gave the image no rating.  After all, how artistic can bits and pieces of four-dimensional elephants be?

Near perfect conditions prevailed here at Fractal Central on Thursday.  The temperature reached a summer-like 86F 30C, the humidity was low, and the kodachrome (digitally enhanced) blue sky was decorated with puffy white clouds.

The fractal cats must have approved, for they spent an unusually long time gazing out the side window, watching the birds fly by. My day, as well as FL's day, was quite busy, which is all well and good, but I still would like more time for fractals.  And speaking of fractals, the next one will be posted in 24 hours.  Until then, take care, and where is the scapegoat?

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


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

Elephant_Pieces    { ; time=0:09:58.90-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1
  center-mag=+0.51519297/-0.01004759/532/0.01382/\
  -0.172917345564469804/-87.8736638009453799
  params=0/0/90/0/0.28/0/0/0.5/2/0 float=y
  maxiter=32767 inside=0 logmap=20 periodicity=6
  colors=0008Kt8Ks8Kr8Kq8Kp8Ko8Kn8Km8Kl9JkAIjBHiCGhD\
  FgEEfFDeGCdHBcIAbJ9aK8`K8_K7YM6WO5VQ7TSATUDWWGZYJa\
  _MdaPgcSjeVmgYpdWp`UpXRpTPpPNpLLpIJpMLqQMrUNsYOtaP\
  teQucSvaUw_WxYYxW_wUarScmQehOgcMhZKhUIePHcKG`FGYCF\
  WFFTHEQJEOLDLNDJPFKOGKOHLOILNJMNKMNLNMMNMNOMOOLPQM\
  QSNRUOSWPUYQW_RYaS_cTadTceSehVejXelZen`epberdetfev\
  hexjezlcxmbvmatn`rnZpoYnoXloWjpUhpTfqSdqRbqQ_rPXsO\
  VtNStMSuLTvLUvKVwJWxIXxHYyGZzG_zG`yGaxGbxdczeczgcz\
  iczkczfczaczXczSczNczLdzMezNfzOgzPhzQizThzWfz_dzbc\
  zfcziczmczpcztczrczoczlczjczgczdczbcz_mzXmzVmzSmzP\
  mzMmzMmzMmzMmzMmzLmzLmzLmzLmzKmzKmzKzzKzzKzzJzzJzz\
  JzzJzzIzzIzzIzzIzzIzzHzzHzzHzzHzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  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=========================================