Fractal visionaries and enthusiasts: 

Today's fractal subtracts 0.2 part of Z^3 from Z^2 on each iteration before adding C.  The resulting Julibrot has two critical values, one at zero, the other at +3.333...  The two values create the same parent fractal -- close to normal Mandelbrot sets that are oriented at 180 degrees from each other.  Today's image lies in the parent fractal that results when Z is initialized at +3.333...

This parent is the Mandelbrot set rotated 180 degrees.  It has an interesting stem extending west from East Valley and another stem extending east from the main bud.  Today's scene lies near a larger minibrot on the eastern stem, which is along the positive X-axis and has characteristics of the negative stem of the M-set.

The name "Carnival of Fractals" came to me as I was wondering whether to tone down the colors.  I finally decided to leave the colors quite brilliant, which seems to work quite well.

The art rating of an 8 shows that the image is well worth the 1-3/4 minutes required to calculate it on one of today's fireball units that has not lost the ability to run DOS programs.  Those addicted to things like smart phones and apps are out of luck . . . I guess . . .  But don't worry, for the web sites are always ready to charge to the rescue and bring enlightenment.  The math rating of a 6 shows that nothing new is in the mathematical aspect of the image.

A mix of clouds and sun, with more clouds than sun, prevailed here at Fractal Central today, while the temperature of 46F +8C kept the proper pre-Halloween chill in the air.  The fractal cats who are now just starting to accept each other, had little time to notice the weather.  The newcomer, who we have named Jasmine, (Jazzy for short), is now large enough to leap onto many of the old fractal cat's (Nico's) favorite spots.  Nico is not too happy with Jazzy taking over his napping chairs, but he does not seem too angry either.  The humans are mostly letting the dynamic duo work things out for themselves, ready of course to intervene if things threaten to get out of control.

The next FOTD will most likely be posted in about 24 hours.  Until whenever, take care, and the United States, usually referred to as America, is not only the greatest country on earth, but it is always right.  And any country that fails to agree had better watch its step.

Jim Muth
jimmuth@earthlink.net


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

CarnivalOfFractals { ; time=0:01:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=+1.655267462218993/+0.00001248433946918\
  /2.642538e+010/1/117.5/0 params=1/2/-0.2/3/0/0/0/0
  float=y maxiter=1500 inside=0 logmap=-122
  periodicity=6 mathtolerance=0.05/1
  colors=000K0OJ0MI0KH0IG0GF0EE0BD08B05902600300000m\
  rzT7fUFmUOeKGSA8EzKKe6PV4IL3CA16JVkmcmdzYgzzd0KK0K\
  00K85AyXSt2RS1DpWyQGVzgpzzzzzQzCzhzzQ3Lc4GK2821iIe\
  zDQz9Kd45nUE3jsN_aVIJFP50I30C20610iHoN8QakuPWaCGJ0\
  SA0E5QjdJZUDNK6BAyxKTFEE77dUNUMHKFBA75ypHdZBKH5YCL\
  M8EB47t1CtHvAUZ5FH2tW1eO1SG0E85q`3cR2RI1D9hs8sFk`A\
  WI5GmyePVLIKXsiA`U6IF3J0AC06603C5E8pl6b_4QO2DCUUXF\
  FGAtO6aG3J85aZ3SQ2JH1984SA2E5BtK7aD3J6A7mzzXzzGzzL\
  zzEzz7zzvzzgzzTzzEzzdzzpzzQzzzzzVzz6zz4zz3zz2zz1zz\
  VzzKzzAzzzzzjzzVzzFzzvzzTzzpzzZzzHzz`zzUzzUzzUzzUz\
  zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzczzczzczzczzc\
  zzczzczzczzczzczzczzczzczzczzczzczzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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