Fractal visionaries and enthusiasts:

Today's image shows an apparently cubic minibrot caught in the act of anti-iterating, a phenomenon that I recently discovered, or more accurately heard about.   I named it "Planetary Nebula" because it rather looks like one.

Anti-iteration is when the number of elements is repeatedly cut in half as we approach a point of attraction, rather than constantly doubling, as is the case with normal minibrots.   (A planetary nebula is formed when a normal-sized star runs out of nuclear fuel late in its life and puffs off its outer layers in a gaseous shell until it finally collapses into a white dwarf.)

On the surface, the parent fractal of today's image resembles a grossly oversized Mandelbrot set, but deep in its depths everything turns cubic.   Today's scene is located on a filament extending southeast from the main bay of the third largest minibrot on the main stem of the Mandelbrot-like parent, at a depth where everything has become almost but not quite cubic.

The rating of an 8-3/4 includes 1/2 point for mathematical interest and 1/4 point for the coloring.   The calculation time of an incredibly fast 43 seconds will pass in an instant when the top part of the image first appears.   Those with a high-speed connection to the Internet may download the finished image from the FOTD web site at:in even less time.   Those with a dial-up connection may need to wait a few seconds longer.

Clouds, rain and drizzle kept the fractal cats in a sour mood all day Tuesday here at Fractal Central.   The temperature of 48F 9C cheered them none at all.   Only a combination of tuna, turkey and cheese made the duo bearable.

My day was a bit improved however -- the day's work went better than expected.   If the luck holds, the next FOTD, which will be posted in 24 hours, will also be better than expected.   Until then, take care, and if the government gave everyone a tax refund of one million dollars, all our economic problems would instantly be solved as they went out and spent the money.


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Planetary_Nebula    { ; time=0:00:43.63-SF5 on P4-2000
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  formulaname=DivideBrot5 maxiter=1500 periodicity=10
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frm:DivideBrot5   { ; Jim Muth
  z=(0,0), c=pixel, a=real(p1)-2,
  b=imag(p1)+0.00000000000000000001:
  z=sqr(z)/(z^(-a)+b)+c
  |z| < 1000000 }

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