Fractal visionaries and enthusiasts:

Minibrots in fractals are easy to find and very widely known, but much less known are antiminibrots, which are quite difficult to find.  Minibrots lie at the center of a basin where the iteration count increases as the center is neared, and reaches infinity at the edge of minibrot itself.  Antiminibrots are peaks with an area of lowest iteration count at the center.  In today's image the center is beyond resolution, so I cannot give the iteration count at the central peak.  But the count need not be as low as 1.

In a minibrot basin, the number of elements surrounding the central minibrot bifurcates in a 2,4,8,16... series as the 'brot is approached.  In an antiminibrot such as the one in today's image, the number antibifurcates in a 16,8,4,2 series.

In everyday minibrot images, the lowest iteration bands lie around the edges of the frame, and the automatic logmap feature (setting the logmap to 2) works very well, but in antiminibrot images such as today's, where the lowest count is at the center, the automatic logmap is useless.  Luckily, turning off the logmap in today's image works just as well as the automatic feature.

Today's image rates an honest 10.  Its mathematical and coloring values are both well above average.  And its calculation time of 59 seconds can hardly be beat.  BTW, 95-percent of the coloring was created by the Fractint program.  I tweaked only 10 or so color registers.

The name "Great AntiMinibrot" says it all.

The image calculates in less than a minute, but it still takes some time to set up the parameter file.

Partly cloudy skies with slightly lower temperatures and noticeably lower humidity prevailed here at Fractal Central on Sunday.  Nicholas, the fractal cat who dislikes heat, spent most of the day stretched on the cool tile floor.  Cassie, who likes it warmer, passed the day curled on the foot stool.  FL and I spent the day taking it easy.

The next FOTD, probably not as great as today but hopefully still quite good, will be posted in 24 hours.  Until then, take care, and get a new angle on things.

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


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

Great_AntiMinibrot { ; time=0:00:59.09-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip
  center-mag=-0.2382764653067911/+0.6598651051332169\
  /1.26548e+013/1/-15/0 params=6/1e+023/0/0 float=y
  maxiter=2250 periodicity=6 mathtolerance=0.05/1
  colors=000T_IXWMGELHFMIGMJGMKHMKHMLIMMINNJNNJNOKNP\
  KNQLNRLNRMOSMOTNOUNOUOOVOOWPOXPPYQPYQPZRP_RP`SPF8_\
  QIUT3gU5fU6eV7dV8cV9bWBaWC`XD_XEZXFYYHYYIXYJWZKVZL\
  U_NT_OS_PR`QQ`RPmg4ke7jc9ibBg`Df_FeYHcWJbVLaTNvZkt\
  YisYhrXgqXfpXdoWcmWblWakV`jVZiUYhUXfUWeTVdTTcTSbSR\
  aSQAC_NVgOVfPVePVdQUbRUaSU`TU_TUZUTYVTXWTWXTVXTUYS\
  T_SPZSS_SR`SQXubYsaYr`Yp`Yo_YnZZlZZkYZjXZhXZgWZfW_\
  dV_cU_aU_`T__S`YS`XR0mz0kz0iz2gz4ez5cz6az7_z9YzAWz\
  BUzCSzDQzFOvGMrHLmILhJMcLM_MNZNNYOOYOOXNPWNPVMQUMR\
  TLRSLSRKTQKUPJXOI_MKbKMeIOhGQkETnCVqAXt8Zw6ay3ax3`\
  u3_r4Zo4Yl5Xi5Wf6Vc6U`6TY7SV7RS8QP8PM9OJ9NGAMMGLTM\
  K_Szczzazv_wtYtrWqpUnnSklPhjNehKbeH_cEXaCU_9RY6OV3\
  KTAMRHOPORNVTKbWNaXQ_YUZZXX`_VacUbfSciQemPfpNgtLir\
  MioNilOijPigQidRhVKVLCHB42B42B52B52B62B72B72B82B82\
  B92BA2BA2BB2BC2FE8KHFPKMTNTYQ_bTfaTe_TcZTaXT_WTYUT\
  WSTVRTT`SP`SPDp3Hk7LgBPcE }

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