FOTD -- November 12, 2008 (Rating 8.5)

Fractal visionaries and enthusiasts:

Yes, there is a minibrot in the lower part of today's image, and 
there is a less obvious upside-down cubic bud in the upper part. 
And this has anything to do with the number of iterations a par-
ticular point takes before reaching an arbitrary distance from 
the origin.

Escape time is not involved in the image because it consists 
entirely of trapped points that have been made visible by the 
'bof60' inside fill, which colors the points according to how 
close to the origin they come in their trapped wanderings.

The most amazing thing is that the small Mandelbrot set and the 
ghostly cubic bud are actually there at all.  The more I work 
with fractals, the more I come to see the Mandelbrot set as a 
universal presence, created in potential by mankind when he 
invented and defined complex numbers.

With all this in mind, I named today's image "Mystical Mini-
brots".  Of course, only one obvious minibrot exists in the 
image, but I see other brilliant yellow points scattered about. 
Could these be other minibrots?  Only a further investigation 
will tell.

The rating of an 8-1/2 includes a self-awarded half point for 
the effort I expended in getting smooth gradation with only 256 
colors.  The calculation time of 3-3/4 minutes is extrapolated 
from the 14 minutes the image took to run on the P200 machine.  
The 2000mhz unit is still out of action.

The image may also be seen and hopefully enjoyed by surfing out 
to the FOTD web site at:

       

and viewing it without effort there.

Leaden gray skies and a chilly temperature of 43F 6C made 
Tuesday a rather forgettable day here at Fractal Central.  The 
fractal cats again complained when the sun failed to appear as 
scheduled on their shelf in the southwest window.  I eased my 
own gloom by treating myself to a genuine New York egg cream.

The next FOTD will be posted in 24 hours, a fact that hardly 
needs to be repeated.  Until that (IMO) wonderful moment, take 
care, and choose wisely.


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


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

Mystical_Minibrots { ; time=0:03:45.72-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=DivideBrot5 passes=t periodicity=10
  center-mag=-2.5071809/0/91.53/1/-90/0 params=-3/100
  float=y maxiter=1000 inside=bof60 logmap=yes
  colors=000zzzzqmzjcreUmZEcVEUSEOODKMDKLDKMEKKQFFXA\
  Ac55j65j76j86j97jA7jB8jC8jD9jE9jFAjGAjHBjIBjKCjLDj\
  MEjNFjOGiPHhQIgRJfSKeTLdUMcVNbVOaUP`UQ_URZUSYTTXTT\
  WTTVSTUSTTSTSSTRRTQRTPRTOQTNQTMQTLPTKPTJPTIPTHOTGO\
  TFOTENTDNTCNTBMTANS9NSANSBNRDNREOQFOQHOPIOPJOOKPOM\
  PNNPNOPMQPMRPLSQLTQKVQKWQJXQIZRI_RH`RHaRGcRGdRFeSF\
  gSEhSEiSDjSDlTCmTCnTBpTBqTArTAsSBrSCrRDqREqRFpQGpQ\
  HpPIoPJoPKnOLnOMnONmNOmNPlMQlMRlMSkLTkLUjKVjKWiKXi\
  JYiJZhJ_hI`gIagHbgHcfHdfGeeGfeKheQjdWldancgpcmqchk\
  `c`YURVKHSL9PM1MN2NN2NN2NN2NN2NN3NN3NN3NN3ON3ON3ON\
  4ON4ON4ON4ON4ON5PN5PN5PN5PN5PN5PN6PN6PN6PN6QN6QN5P\
  N4OL3NI2MF1ID0FA0A505000N8RN8RN9RN9RN9RN9SN9SN9SNA\
  SNASNASNASNASM9RNASNBSOBSOCTPCTPDTQDTQEURFURFURGVS\
  GVSHVTHVTIWUJWUJWVKWVKXVLXWLXWMYXNYXNYYOYYOZZPZZPZ\
  ZQZ_R__R_`S_`S`aT`aT`bU`bVacVacWacWbdXbdXbeYbeZcfZ\
  cf_cg_cg`dg`dXVEXVEXVDXVD }

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=========================================  


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