Fractal visionaries and enthusiasts:

Today's image could almost be a photograph of a 3-D scene.  Actually, there is nothing 3-D at all about it.  It is totally 2-D, a flat scene in a fragmented elephant in the rudimentary East Valley of the parent fractal that results when the expression Z^(1.5)+C is iterated 12 levels up the logarithmic ladder with the 'round' function applied.

The 3-D effect is a combination of the coloring and the basic underlying iteration bands.  But it is an illusion.  The wrong colors will totally destroy the 3-D effect.

Actually, the visual 3-D view we have of the so-called outer 'real' world is also an illusion.  The images on our retinas are totally 2-D.  The third dimension appears in our awareness when our mind (or brain if you're a materialist) compares and combines the two slightly different images sent to it by our two eyes.

Does this mean that the 3-D solidity of the outer world is also an illusion?  I often wonder.  True, the outer world obeys the mathematical laws of 3-D space, but we ourselves invented mathematics and tweaked its rules so that it works correctly when we apply it to the world we assume exists around us.

We can prove that the universe is three-dimensional by observing the orbits of the planets.  It can be demonstrated mathematically that stable planetary orbits are possible only in spaces of two or three dimensions.  Of course, if we lived in a world of four spatial dimensions, we would have developed a math that demonstrates that stable orbits are possible also in spaces of four dimensions.

Now back to the image.

I named today's image "Marshmallow Design".  I must have had a fleeting impression of roasting marshmallows while trying to think of a name.  The rating of a 9.5 is exceptionally high, and includes a generous self-reward for the coloring, but I think the image is worth it.

The calculation time of 1-2/3 minutes will be no problem for those who cook their own fractals.

Typical summer weather made Thursday a typical partly cloudy summer day here at Fractal Central.  The fractal cats thought the temperature of 88F 31C was a bit warm, but with the cool tile floor to stretch out on, they did not complain too much.  My day was about average.

The next FOTD will be posted in 24 hours.  Until then, take care, and the greedy big-oil guys are getting worried.  So keep pumping and reassure them that we still depend on them.

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


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

Marshmallow_Design { ; time=0:01:40.86-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=round logmap=270
  center-mag=+0.159907326462106/-0.00233287824442478\
  /1.136758e+013/1/-27.9/0 params=1.5/0/12/0 float=y
  maxiter=1500 inside=0 mathtolerance=0.05/1
  colors=0004Ab17c48e79gAAiDBkGCmICoMEmQGiUHdYJ`aLWe\
  MSiONmPJnNIoMHoLGpKGpJFqIEqHDrGDsECsDBtCAtBAuA9u98\
  v87v77vEBzwmyykxxiwwgvvettcrraoo_llYiiWffVccT__RWX\
  PSTOOPMLMKIJIGHGEFECDCABA8986764542321200100000000\
  00000000000AAAKKKUU_ZZYS`VLaTEjRJhSOfSTdSXbSa`SfZS\
  kXSoWSn_QzzczxczuzvszrqmmocdmUXdSPWWGSU8OS0MQ0KO0I\
  M0GKm`5gd9ciEceEcaBhY9mU7rQ5sO7tL6sS5rZ4qe3pl2os1n\
  y1mn5ac9VUDNJHG9KUHLgPMtWMneRhoVbyZRjBPhANf9Le9Jc8\
  Hb8F`7E_7FZEGYKHXQIWWJVbKUhLTnMStV_lcgdloXuwQorSjm\
  TehV`cWWZXRUZMP_HL`KzzzzzEzzmzzEzzmzzDfRDcPIgPNjPS\
  mPXpPasPevPhqSjlUlgWnbYpY_rUalTXfSTaROWQKQPGLOBFN7\
  AM3HK5NJ6TI7ZH8dG9fEDgDHhCLjBPkATl9XjIRhRMf_HdhCcp\
  7UiHKbRBW`FX_IY_LY_OZ_R__U__MdRFiz8nzArzAszAtzFuzH\
  vzJwzzxwzyxzzxzzpzzhzz`zzTzzLWzESzJPzOQzSRzWSz_Tzb\
  UzfzzjzzmzzjzzgzzdzzbzzezzhWza`zVezOjzHozAtz4rzFqz\
  Ppz_oziazVPzHCz3Bz2Bz2Bz2 }

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