Fractal visionaries and enthusiasts:

Believe it or not, today's image is a scene in the Seahorse Valley area of the (-Z)^(1.5)+C Mandeloid.  Actually, the scene is very close to a Julia set of the valley, being double-rotated only 0.4,0.4 degrees from the true Julia direction.  The wedge-shaped feature almost filling the outer figure-8 shape is a grossly enlarged view of the Mandelbrot Seahorse Valley.

Iterating (-Z) rather than straight (Z) makes a great difference in the fractals with a fractional exponent of Z between 1 and 2.  While positive (Z) results in tiny bean-shaped fractals, negative(Z) produces much larger fractals, with recognizable Seahorse Valleys and much more interesting surrounding semi-chaos to explore.

I rendered the scene with the outside set to 'tdis'.  Some of the other outside options also produce interesting versions of the scene.

The name "1-1/2 Seahorses" refers to the exponent of Z, not to any sliced up seahorses that might be lying around.

The rating of an 8 includes a full point for the coloring.  This might be a bit excessive, but why not reward myself?  I must have put almost an hour into working out the colors.

The calculation time of 8-3/4 minutes is on the slow side.  Most of this time is caused by the large maxiter of 32767, which was the maxiter limit of early versions of Fractint, and which I still use as a standard setting.

Heavy clouds and intermittent showers continued here at Fractal Central on Thursday, while the temperature of 63F 17C was on the mild side for the season.  The fractal cats, being warm weather fans, enjoyed the conditions.  The humans spent the day doing routine things, which make for a peaceful day to live through but rather dull reporting.  The next FOTD is scheduled to be posted in 24 hours, and it might actually be ready.  Until next time, take care, and if we ever defeated the terrorists, who would we then blame our problems on.

Jim Muth
jimmuth@earthlink.net


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

1-1/2_Seahorses    { ; time=0:08:47.48-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=t inside=0
  center-mag=-0.305312/0.00434276/1.123196
  params=89.6/0/89.6/92/-0.742/0.05/0/0/1.5/0 float=y
  maxiter=32767 outside=tdis logmap=3 periodicity=9
  colors=000TL_SKYRJWQIUPHSOGQNFOMEMLDKKCIJBFIACH99G\
  86F73D50C30700800900000000000000000000000000ZVKb`D\
  fe6lx_iwaevcbvf_uhWtjTslQsoMrqJqsGpuDpwIqrMrmQshUt\
  cYuZauUzMHvJMsGRpDWlA`i7ef4iY3`P2SG1J71BJ4DU6Fd9Ho\
  BJzDLwJPtPTqVWn`_kfbhlffridojbmk`jl_hmYenWcoV`oTZp\
  RWqPUrORsMPtKMuJKuLMsNNrPPqRQpTRoVTnXUmZWk`XjbYid_\
  hf`ghbfjcekddlbelaem`em_emZejachcbfe`cg_aiY_kXXnWV\
  pUTrTctRmvQzxPmqNcjMScKSXJTQHUJGRKJOKMLKPJKSGKVDLX\
  AL_8Lb5Le2Lh0Lj1Mg1Md2Mb2M_2MX3MV3MS4NP4cc4cc5cc5c\
  c6cc6cc6cc6cc6cc6cc6cc6cc6cf6cl6cr9cpBmoDmnGmlImkK\
  mjNmhPmgRmfUmdWmcomYcmZ9mgwmuqmmkmfemzkmzgmzcmz4mz\
  LmzcmzamzZmz_mz_mz`mzNmzSmzXmzemzcrzarzDrzSrzXrz9r\
  zGrzNrzUrz0rzJrzDrzPrzcrzbrzarzmrzmrzmrzmrzmrzmrzm\
  rzmrzmrzmrzmrzmwzmrzmrzmrzmrzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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