Fractal visionaries and enthusiasts:  

Today's image is another, and probably the last, of the present series of ventures into the world of the four-dimensional HyperMandelbrot set.  To create the image I took the image of March 4 and decreased the value of the real(p4) parameter to 1e-170.  As a result I found that the number of arms surrounding the center point, which is the pseudo-origin of the underlying minibrot, has increased.

I'll make no effort to explain the number of elements around the center, since I have no idea what determines this number.  But the number does appear to increase by increments of two as we venture deeper into the apparently limitless center point.

The color palette is the same one that appeared in the March 4 image, with a few tweakings to smooth some rough breaks.  The rating of 7-1/2 is a bit conservative, but this is the third image based on the same theme, which detracts from its worth.

The calculation time of 2-1/2 minutes is a fair price for the image.  And as always, the web sites are even more fair.

The day began with rain here at Fractal Central.  The rain ended by midday, but the clouds hung on all afternoon.  The temperature of 50F 10C was pleasant enough.  The fractal cat spent the morning watching the world go by and passed the afternoon wrapped in an afghan and visible as only a lump.  The humans passed the day pondering existence.

The next FOTD will be posted in a day or two.  Until whenever, take care, and let a smile be your umbrella on a rainy day, but don't start complaining when you get wet.

Jim Muth
jimmuth@earthlink.net


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

More_Vacuum_Energy { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 center-mag=+0.2587410\
  516089257/-0.0013438824741138/8.974e+009/1/-162.5/0
  params=0/0/0/0/1/0/1e-170/0 float=y maxiter=3200
  inside=0 periodicity=0
  colors=000QDFSEFUFFWGFYHF_IKaJQcKWbIebGgbEpdFrfGzh\
  GziHwjIziJziKziKzkLzkMzmNznOznMznOzmPwmRtmVqnXmo_h\
  pccrhZtl_vojxpzpmcfajWSPPLQMGQLEMLERJFSHHSIITKJTML\
  WOLYQMYSM`UNcVNfWOiXPlYRoZUr_Wv`Zya`yc`zd_zfYtdWqe\
  RocMiaId_F`YCXW9TX6SX3SY7SYASZESZIS_MS_PS`TS`XSa`S\
  acSbgSbkSfoQbnSZpTVsVSqWOqXKoZGm_Dk`9ib5gc2edNdbRd\
  `UeZXeX_eVbeTebRh_PkXNnUMlSNjRNiQNgONeNNdMObLO`JO_\
  IOYHORDPXGObJNcMMcPLcPKcPIcOHcUGcUFcUDcUCcUBcUAcU8\
  cU7cU6bU5`U3_U2YU1XU0YU2ZU3WU1ZV4`V7bVAdVCfVFhVIkU\
  KmUNoUQqUSsUVuUYwU_qZXkbVeaS_`QVZOPZLJZJDZG7ZE2ZC4\
  ZF6ZI8ZKAZNCZQDZSFZVHZYJZ_LZbLZfMZdM_cNaaNY`NU_OPY\
  OLXPNVPPUOPVPQTPRRQRPQTNRUMRWKSWISWGTWETXDUYBUZ9VZ\
  7YY2VX6SW9PVCQUDRUDSUETSETQFUPFVMGWJGXHHXEHYBIZ9I_\
  6J`8JaAK`CJ_EI_GIZIHYKHYMGXOGWQFWSEVUEUUDUUDTUCQUB\
  TUCVUCYUC_UCbUCdUCfUDiUDkUDnUDpUDqU8rUDrUHrWLsYPs_\
  Ts`YC6FE7FG8FI9FKAFMBFOCF }

frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }

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