Fractal visionaries and enthusiasts: 

Today's image shows what happens in the fractal that results when the whimsical expression (Z^1.5)+(1.5*Z^2)+(2*Z^2.5)+(2.5*Z^3)+C is iterated with Z initialized to the assumed critical value of -0.3968...  Zero appears to be a second critical value, but I have not yet checked this fractal.

The parent fractal of today's image looks not at all critical.  It consists of little more than a roughly circular open bay with an area of sandy debris along its western shore line.  So far, so good, but look at today's image, which shows what lies buried not very deep in this debris.

About 15 years ago I discovered a near-perfect rectangle.  In today's image I have found a near-perfect equilateral triangle.  This raises the math value to a superior 9.  With little more than sand, not very attractive filaments, hurried coloring and a triangle going for it, the artistic worth remains mired at a humdrum 5.

The name "The All-Seeing Eye" came to mind when I happened to notice the back of a one-dollar bill, which has the image of an unfinished pyramid with an eye printed on it.  I guess the Masons are in town.

The calculation time of 1-3/4 minutes will pass in two flashes, even faster on the FOTD web sites.

Much cooler air brought a refreshing relief to Fractal Central today.  With a mix of clouds and sun, a temperature of 70F 21C and much drier air, the day could hardly have been improved upon.  At least the fractal cat thought so.  The humans always find a way the day could have been better however.

The next FOTD will be posted, that's a promise, but there is no guarantee of the exact time.  Until whenever the time comes, take care, and see you then.

Jim Muth
jimmuth@earthlink.net


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

The_All-Seeing_Eye { ; time=0:01:45.00 SF5 at 2000MHZ
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  formulaname=MandelbrotMix3a function=ident float=y
  center-mag=-0.6614804957/+0.0746736023/5347/1/-119\
  /0 params=1/1.5/1.5/2/2/2.5/2.5/3/-0.3968321221967\
  /0 maxiter=1000 inside=0 logmap=29 periodicity=6
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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=========================================