[Fractint] FOTD 09-06-03 (This is How Low [5])

9 Jun 2003

      FOTD -- June 09, 2003 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image takes us to the bottom of the barrel, way down to 
the land of Z^(1.009)+C.  At this abysmal depth, the sand-like 
fractal material has reached such a high maxiter that it is 
effectively beyond reach.  But the areas of extreme discontinu-
ities continue to multiply, and though still of a very high 
maxiter, are within reach for those with patience.  The 'recip' 
function was an accident.  The 'floor' function works best with 
this formula, but the image is good, and who's complaining.

In today's fractal, the coloring makes the picture.  A very 
broad palette is necessary to add definition to an otherwise 
featureless image, but when this is done, a series of feathery 
curving arms appears.  I have named the image "This is How Low" 
because its exponent of Z is about as close to unity as it is 
possible to come and still get something other than an empty, 
featureless circle.

I have rated the image at an average 5, more for mathematical 
interest than for artistic worth.  If it were not for the render 
time of over 2 hours on my machine, the image might have rated 
a 6.  But don't be put off by the slowness of the image.  Give 
Paul and Scott a couple hours to render the image, then visit 
their web sites to download the completed image.  Paul's site is:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Scott's is:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The rain held off on Sunday here at Fractal Central.  Despite a 
temperature that never reached 70F 21C, the fractal cats had a 
good day.  When the cats are happy, I'm happy also, so I also 
had a good day.  Today is actually starting with some sun, and 
no rain is forecast, making another good day near certain.

Once the day's work is behind me, assuming the cats are happy, 
my day should once again be good.  Tomorrow's FOTD might launch 
out in a new direction, or it might be a return to the 
MandelbrotMix4 formula and the midgets it draws.  To see what 
happens, check back in 24 hours.  Until then, take care, and 
hope for the best.

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

START 20.0 PAR-FORMULA FILE================================

This_is_How_Low    { ; time=2:05:42.24--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=mandelbrotbc1 function=recip passes=1
  center-mag=+0.07536313779841985/+0.000859404003554\
  35/8654862/1/51/-1.76329913170736319e-009
  params=1.009/0/-182/1000 float=y maxiter=12000
  inside=255 logmap=3216 periodicity=10
  colors=000zlPzmQzmQzmQzmQzmRzmRymRymRymRymSxmSxmSx\
  mSxmUwmTwmSwmSwmRvmRvmQvmQvmPumPumOumOumNtmNtmMtmM\
  tmLslKskKsjJsiJrhIsgItfHueHvfGwfGxgFygFwhEwhEwiDwj\
  CziDziDzhDzhDzgEzgEzfEzfEyeExeFwdFvdFucFtcGsbGrbGq\
  aGpaGo`Hn`Hm_Hm_HmZIlZIlYIlYIlXIlXJlXJlWJlWJkVJkVK\
  kUKkUKkTKkTLkSLkSLjRLjRLjQMjQMjPMjPMjONjONiNNiNNiM\
  NiMOiLOiLOiKOiKPhJPhJPhJPhIPhIQhHQhHQhGQgGQgFRgFRg\
  ERgERgDSgDSgCSfCSfBSfBTfATfATf9Tf9Uf8Ue8Ue7Ue7Ue6V\
  e6Ve5Ve5Vg3Wf4Ve5Ve5Vd6Ud6Uc7Uc7Tb8Ta8Ta9S`AS`AS_B\
  R_BRZCRYCQYDQXDQXEPWFPWFPVGOUGOUHOTHNTINSINSJMRJMQ\
  KMQLLPLLPMLOMKONKNNKMOJMOJLPJLQIKQIKRIJRHISHISHHTG\
  HTGGUGGVFFVFEWFEWEDXEDXECYDCYDBZD9YCBZDC_DD_DE`EF`\
  EGaEHaEIbFJbFKcFLcGMdGNdGOeGQeHRfHSfHTgHUgIVhIWhIX\
  iJYiJZjJ_jJ`kKakKblKclKclJblJalJalJ`lI_mI_mIZmIYmH\
  YmHXmHXmHWmGVmGVmGUmGTmFTmFSnFRnFRnEQnEPnEPnEOnDNn\
  DNnDMnDLnCLnCKnCJoCJoBIoB }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

END 20.0 PAR-FORMULA FILE==================================