Fractal visionaries and enthusiasts:  

The name of today's image asks a question -- "How Low Are We?"  The real(p1) parameter answers that question.  The exponent of Z in today's image lies at the lowly level of 1.067, a level where fractals would normally be assumed to be virtually impossible, much less filled with minibrots.  But thanks to the overworked MandelbrotBC3, which calculates the multiple values of the complex-log function, we have not only a fractal, but a rather exciting minibrot.

The parent fractal resembles an orca swimming freely through its natural habitat, the ocean.  The fractal orca is surrounded by a cloud of sandy debris that could be bubbles.  Today's scene is located in this bubble debris, to the lower left of the orca.

The minibrot in today's image is shaped like a plunging rocket ship, not at all like the orca shape of its parent.  Almost all minibrots in this ultra-low range of exponents of Z are shaped like rockets or torpedoes, but this does not mean the scenes are worthless.  The features surrounding the minibrots can sometimes be surprising.

The art worth of today's image rates a 7.  In my opinion, the art aspect is notably above average, held up by its brilliant coloring.  The math rating of an 8 points to the surprise of finding a minibrot in a fractal with an exponent of Z as low as 1.067.  And this is not the lowest possible exponent that would produce a fractal with minibrots.  Like all things fractal, there is no well-defined cut-off point below which fractals with minibrots are impossible.  Finding them simply becomes ever more difficult until the fractalist simply stops his search.

The maxiter of today's image is 420,000, which results in a calculation time of 7-1/2 minutes.  This is a good example of the increasing difficulty as the exponent approaches unity.  And even with this extreme value, the minibrot is far from fully resolved.  Luckily, the web sites are there to bring relief.

Today brought a mix of clouds and sun, brisk winds and a temperature of 61F 16C to Fractal Central.  The fractal cats, now quite difficult to tell apart from a distance, had a playful day.  The humans had a work day.  The next FOTD will be delayed until May 4, two days from now.  Until then, take care, and I just found a mind hiding under the stairs.  Did anyone lose theirs?

Jim Muth
jimmuth@earthlink.net


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

How_Low_Are_We?    { ; time=0:07:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident passes=t
  center-mag=-7.525986636549002/-3.471416076886733/\
  3.47627e+010/1/110/0 params=1.067/0/0/1500 float=y
  maxiter=420000 inside=0 logmap=395
  colors=000d00b00`00_00Y00U02R0GT1JU5LW7MYCO_ER`JTb\
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  zY_zOJzD5z50y00w00s00o00l00g20d60`A0YD0UH0RM0OP0PM\
  1RJ5TGAUEGWCLY9R_6W`5giMusfln_dgTYbMRYGLTALMDLHEGD\
  GA9H55J01L50MA0OF0LK0HP2EV5C`79bA6fD4iH2nP0qY0sd0w\
  d0zo0zuczyzzzz2PH5PH7PH9PHCPHDPHGPHHPHLPHOcYPcYTcY\
  UcYYcY_cYbcYdcYbcobcobco`co`co`co_co_co_ozYozYozYo\
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  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  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=========================================