Fractal visionaries and enthusiasts:

As long as one does not look too deeply into the parent fractal of today's image, it appears to be an everyday Mandelbrot set, but in its depths a certain strangeness starts to creep in.  The surface minibrots are perfect miniature M-sets, but as we go deeper, the minibrots become confused, as though they are undecided whether to be quadratic or quintic miniatures.  Then, when we reach the deepest depths, the minibrots are purely quintic, with the four lobes and everything else expected in such minibrots.

Normally, quintic minibrots are rather boring things, with a tendency to all look the same, but the minibrot in today's image is far from boring.  Minibrots usually lie at the center of a basin, with the iteration count steadily increasing as the minibrot is approached.  Some minibrots in fractals created with certain formulas, such as the minibrot in today's image, are like volcanoes however -- rising mountains with deep craters at their peaks.  As we near these minibrots, the iteration count first decreases gradually, then rises rapidly as we approach the minibrot itself.  The reddish parts of today's image are the lowest iteration stuff.  The sky-blue stuff behind the dark blue blobs surrounding the flat circular red ridge, as well as the stuff near the minibrot, is the actual high-iteration stuff.

The image is located in the trunk of the period-10 elephant on the southeast shore line of the parent M-set.  It is quite close to the limit of resolution, which makes the 'mathtolerance' entry necessary in the included parameter file.  The name "Chaos Incorporated" expresses my impression of the background areas surrounding the red mountain.

The rating of a 7-1/2 includes a half point for the coloring, which is a not-insignificant part of the image.  (My modesty prevents me from rewarding myself with more than a half-point bonus.)

The calculation time of 2-1/3 minutes is a fair price for such a curious image.  The image may be seen for free on the currently active FOTD web site at:

http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html

The original FOTD web site, not up to date, may be seen at:

http://www.Nahee.com/FOTD/

Lots of clouds filled the skies over Fractal Central on Saturday, while the temperature hung around 27F -3C.  Light snow also fell most all day, but by evening had amounted to no more than 1cm.  The fractal cats complained about the lack of sun and then found comfort on the shelf over the hall radiator.

My day was enjoyably slow.  We needed the rest after the hectic days of the past few weeks.  The next FOTD will be posted in 24 hours.  Until then, take care, and be in there with the big time thinkers.  (I leave it to the individual to decide who the big time thinkers are.)

Jim Muth
jamth@mindspring.com


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

Chaos_Incorporated { ; time=0:02:23.30-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip passes=1
  center-mag=+0.3438119752193327/-0.0560302035781458\
  /2.973926e+013/1/-12.6/0 params=5/10000000000.0/0/0
  float=y maxiter=1250 inside=0 logmap=164
  periodicity=6 mathtolerance=0.05/1
  colors=000zhdzkfwkftmhrokmrmktohtodwrbxtZzwXzxVzzR\
  zzPzzNzzJzzHzzFzzVZXh11x00w00t00r00o00m00m00k00h00\
  f00d00d10f00h00h00k00m00m00o00o00r01t0Kt0Uw0cw0mx0\
  mz0iw0ft0cq0`n0Tj0Le0D_07V01Z04`05a07d0Ag1Ci2Dk4Fm\
  7Jo8LrANrDRtFTtHVwJXxN`xPbzRdzTfwRhrRhmRhhRkdRk`Rk\
  XRkTRmPRmLPmHPmDPoAPo7Po4Po1Pr0Pr0Pr0Pr0Tt0Vw0Xw0Z\
  x0`x0bz0dz0fz0hz0kz0mz0oz0rz0tz0wz0xz0zz0zz0zz0zz0\
  zz0xw4tkAo`HkRNfJVbAbZ2kV0tR0zP0wR0tT0rV0oV0mX0kZ0\
  h`0f`0db0bd0`f0Zf0Vh0Tk0Rm0Pm0No0Lr0Jt0Ht0Fw0Dx0Cz\
  0Az0Dt0Fm0Hf0J`0LV0NP1PL4TF5VA8X5AZ1D`0Fb0Jd0L`0NX\
  0NT0NR0NN0NJ2PH4PD5PA8P8AP5CP2FR1HR0LR0NR0PR0TT0VT\
  0XT0`T0XT0TT0PV0LV0HV0DX0AX07X04X01c01h01c01r01e01\
  j01e01x01g01n01g01x01i01n01i01z`kz`kz`kz`kz`kz`kz`\
  kz`kz`kz`kz`kz`kz`kz`kz`kz`kzwwzwwzwwzwwzwwzwwzwwz\
  wwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzww\
  zwwzwwzwwzwwzwwzwwzwwzwwz }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

END PARAMETER FILE=========================================