Fractal visionaries and enthusiasts: 

How low can you go?  No, we're not talking about the long-gone fad of limbo dancing, the lowness lies in today's exponent, which is the 128th root of 2 or 1.0054298, a value so close to unity that its graph is barely distinguishable from a straight line.  But thanks to the MandelbrotBC3 formula, and also the multi-valued nature of the complex log function, we have dredged up something from almost nothing.

True, today's image consists of nothing more than arcs filled with smaller arcs all the way down, but the screen is not filled with a flat pattern and a smooth-edged boundary.

The art rating of a 5 is everyday average.  The math aspect has more interest, and rates a 7, which is somewhat above average.  The name "The Absolute Limit" refers to my present feelings about the low-exponent theme.  It does not mean I will never try to find detail in a fractal with an exponent of 1.0027112, but it does mean that if I ever do go searching, it will not be for a while.

With a running time of 4-1/4 minutes, the calculation is a bit on the slow side, so if time is a factor, check the web sites.

A mix of sun and clouds with a temperature of 46F +8C and a calm wind made today rather pleasant here at Fractal Central.  The fractal cats spent their waking hours getting to know each other better and their sleeping hours asleep.  The fractal humans, if that's what we are, spent the day doing routine things.

The next FOTD will be posted in the near future.  Until the near future arrives, take care, and have you heard the conspiracy theory about the existence of conspiracy theories?

Jim Muth
jimmuth@earthlink.net


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

The_Absolute_Limit { ; time=0:04:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-14.7101/1.17509/8.709171/1/19.25/0
  params=1.0054298/0/0/2400 float=y maxiter=2000
  inside=255 logmap=405 periodicity=8
  colors=000D880000000000000000000000000000000050080\
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  850A50D50E50J60M81P95UAAXCG_DMcERhGXkHcoJiwJhrKfmM\
  dhOccPa_R_WSZRUXMWXJW_DUa9Sc4Rf0Ph0Oi0Of0Jc4Ea9AZG\
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  zzaz0azzaz0azzaz0azhrzcrzZrzUrwRrrMrmHriardarZaraa\
  rdarharkryorzwrzrrzmrzirzfrzarzZrzWrzPrzSrzUrzXvzZ\
  yzazzczzfzzhzzizzZzzPzzMzzazzizzrzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-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 PARAMETER FILE=========================================