Fractal visionaries and enthusiasts:

NEW FORMULA!

Giving in to curiosity, I spent most of the day writing a new version of the SliceJulibrot formula, which applies the MultiExp expression to the four-dimensional Julibrots it draws.  The formula appears on the list today for the first time.

Getting the formula to work took up most of the day's fractal time, so the image I finally found is not much of an example of what the formula might be able to do.  Tomorrow's image should be better however.

I named the image "A Strange Mini Indeed".  Actually, it's not a minibrot, nor is it a Julia set.  It's a hybrid, sliced in the Oblate direction, determined by the imag(C) and real(Z) axes.  Some directions in the image are Mandelbrot, others are Julia, most are somewhere in between.

The parent fractal is an oversized Mandelbrot set corrupted in its depths by order-7 energies.  Today's scene is located well off to the side of the east edge of the large minibrot on the main stem of the parent, in the real(Z) direction.

Some stretching and skewing was needed to eliminate the natural distortion of the image.  This distortion exists in nearly all the odd planes of the Julibrots, and can be only partially eliminated by stretching trickery such as I used in today's image.

The rating of an 8? is a guess, based on what the formula might have in it.  The mathematical interest is there, though the artistic worth of at least today's image leaves something to be desired.

The calculation time of a speedy 38 seconds means that little effort will have been wasted if the image lays an egg.

Morning clouds led to afternoon rain here at Fractal Central today.  The temperature of 39F +4C was mild enough to keep away all danger of ice.  The fractal cats, who wish they had the outdoor life of the old, now departed, fractal cats, would have preferred more sun.  The humans, FL and I, simply made it through another day, which sounds boring, but actually is not.

The next FOTD will be posted in 24 hours.  Until then, take care, and everything looks richer in the fullness of four dimensions.

Jim Muth
jimmuth@earthlink.net

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

AStrangeMiniIndeed { ; time=0:00:38.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot6 function=recip float=y
  center-mag=-1.566172639248917/-0.00216596994206138\
  /8873.693/0.4301/3.2405430019023771/0.0379459741\
  650980814 params=7/10/0/0/90/0/-17.4550736/0/0/0
  maxiter=1800 inside=255 logmap=34 periodicity=6
  colors=00000G00I00K00M00O00Q00S10U30W50Y70_A0aC0cF\
  0eG0dI0cK0bN0`P0ZS0YT5WWDUYKT`URbcPZmO`rMbxKcyJbxK\
  axLaxL`xM_xN_xNZxOZwOYwPXwQXwQWwRWwRVwSUwTUvTTvUTv\
  USvVRvWRvWQvXQvXRsVRqTRnRSlQSiOSgMSdKTbJT_HTYFTWES\
  XGRYIRYJQZLQZMP_OO`QO`RNaTNaUMbWLcYLcZKd`KdaJecIfe\
  IffHghHgiGhkFimFinEjpEjqDksCluCpvBjxBkyAcmATaACQ09\
  E033012U01i01U01E01F_1F01Gc3Ha4mz5JY7KW8LU9MSBNQCO\
  ODOMEPKDQJDRICRHCSGBTFBTEAUDAVCAVB9WA9X98X88Y77Z67\
  Z57Y78Y99XB9XDAWFBWHBVJCVLDUNDUPEURETTFTVGSXGSZHR`\
  IRbIQdJQfKPhKPjLPkLpz9oyAoyBoyCoyDoyEoyFoyGoyHoyIo\
  yJoyKoyLoyMoyNoyOoyPoyQoyRoySoyToyUoyVoyWoyXoyzoyz\
  oyzoyzoyzoyboybnwcmudlsekqfjogimhhkigijfhjefkddlcb\
  mb`naZo`Xp_VqZTrYSrXRoWQlVPiUOfTNcSM`RLYQKVQKSPJPO\
  IMQHJSGGUFDXEA_D7bC4eC1iE2mF2mG2mI2mJ2mK3mM3mN3mO3\
  mP3mRmmSmmTmmVmmWmmXmmZmmYmzXzzWzzVzzVzzUzzTzzSzzR\
  zzRzzQzzPzzOzzOzzWzzVzzUz }

frm:SliceJulibrot6   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p2*0.0055555555555556),
  b=pi*imag(p2*0.0055555555555556),
  g=pi*real(p3*0.0055555555555556),
  d=pi*imag(p3*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a),
  aa=-(real(p1)-2), bb=imag(p1)-0.0000000000000000001,
  c=p+flip(q)+p4, z=r+flip(s)+p5:
  z=z*z*fn1(z^(aa)+bb)+c
  |z|< 100000000 }

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