Fractal visionaries and enthusiasts: 

The farther I delve into these 4-part fractals, the more interesting they become.  It's too bad I'm not math literate enough to write a formula that will automatically initialize Z to one or all of the critical points like the 10-year-old 2-part MandAutoCritInZ formula does.  But the parabolic-plane method I use works well enough.

Today's curious image was created with a combination of straight Z, (1/Z), Z^2 and Z^3, with initial Z set to a critical point of 0.6029...  The resulting parent fractal resembles the eastern third of the main bay of an oversized Mandelbrot set, with an entire skeletal M-set where the rest of the bay should be.  Today's scene lies in the north branch of the strangely solid Seahorse Valley of this skeletal M-set.

There is not much to be said for the image, which speaks well enough for itself, even without being turned into fractal 'music'.  If I had more time to work on the colors, the art aspect of the image might have rated more than the actual 7.  The math aspect remains a 6, which is good enough.

I named the image "Mutated Seahorses" because of the unexpected transformation the seahorse elements have undergone.

The down side is the calculation time of 5-3/4 minutes, which will start to drag, especially on slower machines.  The drag may be eliminated by visiting the FOTD web sites.

Cloudy skies, a few small drops of rain, and a temperature of 64F 18C kept spirits under control here at Fractal Central today.  The old fractal cat was too busy checking the 7-week-old new fractal cat through a cracked door to pay much attention to the weather, while the humans kept an eye on the feline situation.  So far, the two have not decided what they think of each other.

The next FOTD will be posted when the right cosmic time arrives.  Until then, take care, and what are skeptics the most skeptical of?  Is it space aliens visiting earth in UFO's, bigfoot creatures, lake monsters, mental telepathy, spontaneous human combustion, ghosts, reincarnation, the existence of a conscious and transcendental creative power called God, or everything without the solid approval of conventional materialistic science?

Jim Muth
jimmuth@earthlink.net


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

Mutated_Seahorses  { ; time=0:05:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotMix3a function=ident passes=1
  center-mag=-0.9416268908362115/+0.0097462448978816\
  /6.419e+010/1/40/0 params=0.5/1/0.5/-1/0.5/2/0.25/\
  3/0.602906705069/0 float=y maxiter=1600 inside=0
  logmap=249 periodicity=6 mathtolerance=0.05/1
  colors=000lgcjfage_edYcbWa`UYWRVSPSNLPJINGFJCBF97A\
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  jjrkmrlprmsrouqprpqoorlnsinvfmvclv`kvYkvWkvTkvRkvP\
  kvNkvLkvJkvHkvEkvCkvAkv8kv6kv4kv2fvBbvKYvSUv`QvhSv\
  gTvgUvgVvgWvgXvgYvgRvNQvI }

frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }

END PARAMETER FILE=========================================