Fractal visionaries and enthusiasts:

Today's image is an afterthought.  On Friday I was exploring the (-Z)^(1.5)+C Mandeloid, with no thought of finding a FOTD there, but when I stumbled upon today's image, it struck me as so unusual that I decided to declare it FOTD for October 30.

Actually, what we have here is a scene in the Mandeloid that results when the formula is iterated with Z initialized at -0.5. I named the image "Reciprocal World" because of the apparent negative curvature of the surface at the bottom of the frame.  If this were a real planet, it would be in the shape of a pseudosphere.

The rating of a 6 makes the 4-1/2 minute calculation time barely worth the effort.
Friday turned blustery here at Fractal Central, with alternating periods of sun and heavy clouds, and even a few light showers.  The temperature of 48F +9C was too chilly for the fractal cats, who grew tired of watching the blowing leaves and spent most of the day sleeping near the heat or asking for their treats.

My day was slightly busy, but nothing to get excited about.  The next FOTD is due to be posted in 24 hours.  But if an unexpected antiquing trip comes up on Saturday, it could be dalayed however.  Until whenever, take care, and be filled with wonder.

Jim Muth
jamth@mindspring.com


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

Reciprocal_World   { ; time=0:04:26.88-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=1 float=y
  center-mag=-0.0079014/+0.7369293/90/1/-72.5/0
  params=0/0/0/0/0/0/-0.5/0/1.5/0 maxiter=24000
  inside=0 logmap=-120
  colors=000KAHKAIKAJKAKKALKBMKCNJDOIENHFMGGLFHKEIKD\
  IJCIIBIHCIHAIIDHJEGKEFLFEMFEMHFNJFNLGQNHUPKZRMcSOh\
  UQmWSrYUv_VzaWzbWzdWzfXzhXzjXzlXzmXzlYzlZzl_zk`zka\
  zkbzkczjdzjezjfzifzigzihziizhjzhkzhlzgmzgnzgozgozh\
  pzipzipzjpzkqzkqzlqzmqzmrznrzorzorzpszqszqszrszztz\
  ztzztzztzzuzzuzzuzzuzzpzzkzzfzzazzYzzXzzWzzWzzVzzV\
  zzUzzTzzTzzSzzSzzRzzQzzQzzPzzPzzOzzNzzNzzMzzMzzLzz\
  LzzJzzHzzFzzEzzEzzEzzEzzEzzEzzEzzAzzEzzHzzKzzOzzRz\
  zUzzYzz`zzczzgzzjzzmzzqzzszzrzzpzzozznzdmzekzfjzfi\
  zggzgfzheziczibzjazj`zkZzlYzlXzmVzmUznTznSzlUzkVzj\
  XziYzhZzg`zfazebzddzcezbfzahz`iz_jzZlzYmzXnzWpzVqz\
  UrzSqzRqzPpzOpzNozLozKnzJnzHmzGmzFlzDlzCkzBkz9jz8j\
  z6kz7jz8jz8jz9jzAjzAizBizCizCizDizEhzEhzFhzGhzGhzH\
  hzIgzIgzJgzKgzKgzLfzMfzMfzNfzOfzOfzPfzPgzQgzQgzHdz\
  QgzZjzgmzppzxszxqzxpzxnzxmzxkzxjzxhzxgzxfzxdzxczxa\
  zx`zxZzxYzxXzuYzsYzqYznYz }

frm:SliceJulibrot5   {; 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=========================================