Fractal visionaries and enthusiasts:  

Today's image is a scene in yesterday's 'phantom' parent fractal, which was revealed by switching the value of initial Z of the Feb. 18 image to the second critical value of the generating function, which is -1.  The location is near a larger minibrot in a tiny valley on the western shore line of the large western bay of today's parent.

Today's parent fractal, which appeared as yesterday's FOTD, is quite unusual.  It is filled with minibrots, but the minibrots are not the expected quadratic variety as they are in the other parent fractal of today's function.  Instead, as is illustrated in today's image, they appear to be of an order somewhere around 2.5.  Actually, today's entire parent is strange, and deserves a more careful examination, which I will do in the next few days.

The rating of an 8 is divided half-and-half between mathematical interest and fractal artistic value.  The name "In the Phantom" describes the location of today's scene -- in a fractal that first appeared as a buried 'phantom' fractal in the background of the image for February 18.

The calculation time of 6-1/2 minutes is slow.  Checking the web sites can cut the wait to seconds.

A mix of sun and clouds, complete with a few flakes of snow, made today a typical sample of midwinter weather here at Fractal Central.  The temperature of 34F +1C was almost exactly average for the day.  The fractal cat spent several hours on the shelf in the southwest window, trying to enjoy the off-and-on sun, while the humans passed the day working.  The next FOTD will be posted, that much is certain.  The only question is exactly when it will be posted.  Until whenever, take care, and have fun.

Jim Muth
jimmuth@earthlink.net


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

In_the_Phantom     { ; time=0:06:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=cosxx inside=1
  center-mag=-1.759337223588773/+0.04880086507460096\
  /1.244e+010/1/-97.5/0 params=-2/2.3/1/4.6/-0.02/0/\
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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