Fractal visionaries and enthusiasts:

What does today's image have to do with East Valley?   It has everything to do.   There are 12 east valleys in the image.   The tip of the 12 spikes at the top of the scene are actually 12 of the 10-million east valleys spaced evenly around the edge of an order 10,000,001 minibrot.

On my screen the spikes at the top of the image are about 3cm apart.   Since there are 10-million spikes around the perimeter of this minibrot, its circumference must be 30-million centimeters, which gives a diameter of about 10-million cm.   Since there are 100,000 centimeters in one kilometer, the diameter of the entire minibrot at the scale of the image must be about 100 kilometers or 63 miles.   No wonder the tiny bit of the minibrot that fits on the screen appears to have a straight edge.   It's the same reason that the surface of the earth appears flat.

Another curiosity is the detail inside the 12 spikes.   At first glance, this detail appears to be identical in every spike, but actually it changes slightly in each spike.   What an interesting trip it would be to circle the entire minibrot and watch the detail in the 10-million spikes gradually cycle through its series of changes.

The elements at the top of the frame are made of order-10000001 stuff, which changes very slowly.   The elements at the bottom of the frame are quadratic stuff however, and down here the changes come fast.   And yes, there are countless smaller near-circular minibrots in the image.   The most obvious one lies in the lower right quadrant.

 I named the image "One Long Shoreline" after the 300-kilometer shoreline of the minibrot whose edge appears at the top of today's image.   I rated the image at an 8 because that's what I think it's worth.

The calculation time of 4-1/2 minutes is well within reason.   But if you decide to calculate the image, don't become concerned when nothing shows up for a minute or so.   The top several lines are blank black.

As always, the finished image is posted for immediate and total gratification on the FOTD web site at:
Picture perfect weather prevailed here at Fractal Central all day Monday, while the fractal cats, Nicholas and Cassie, took it easy.   (For the exact conditions, picture an absolutely perfect day at your favorite spot on earth.)   At one point, Nicholas, apparently having forgotten the talk he had with the doctor when he was a kitten, got a bit frisky and started yelling like a lovesick tomcat.   A quick serving of half-and-half settled him down and reminded him of what the doctor had told him.

My day was un-eventful.   With only a modicum of luck, tomorrow will be the same.   The next FOTD will be posted in 24 hours.   Until then, take care, and wouldn't life be dull if rational-thinking skeptics were right when they claim the paranormal does not exist?   (Of course, this in no way implies that I think the skeptics are wrong.   I know they are wrong, even though they are convinced they are right!)


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

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

One_Long_Shoreline  { ; time=0:04:30.40-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=NewDivideBrot function=recip logmap=157
  center-mag=-43.09731830432293/+56.66689961740695/2.\
  21687e+010/1/110.34/0 float=y passes=1 maxiter=4000
  params=10000001/100 inside=0 periodicity=10
  colors=000`I4_H6YG8XFBVEDUDFSCGQBINAKLALIANGAQDARB\
  AT7BV6DW5FY5I_5Lb5Ld5Nf5Og5Oj5Pm5Rn5So5Tn5Rn5Pl5Pk\
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  wSIwPKvNKvJKvGKtD4t90s60s20q10q42p78pBDnDInGLlJQlN\
  VkP_kTbiWgiYlg`qgdtfgyfjzdkzblzdmzdnzdozdpzfqzfrzf\
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  9kK7kKDbKDbKDbKDbKDbKDbKDbKDbKDVKDVKDVKDVKDVKDVKDV\
  KDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKD\
  VKDVKDVKDVKDVKDVKDVKDVKDV }

frm:NewDivideBrot   { ; Jim Muth
  z=(0,0), c=pixel, a=-(real(p1)-2),
  b=imag(p1)+0.00000000000000000001:
  z=z^2*fn1(z^(a)+b)+c
  |z| < 1000000 }

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