Fractal visionaries and enthusiasts:  

With today's image, we enter hyper-land.  The image shows an under-resolved high-order 'star' on the southern shore of East Valley of the HyperMandelbrot set.  If the fractal were the classic 2-D Mandelbrot set, the brilliant orangish area in the center would be a large circular black area consisting of inside points whose ultimate escape was missed because they lie beyond the relatively small image maxiter of 580.

But this is not the classic M-set, and something strange has happened.  What should be a blank open area has been filled in by strange new stuff unlike anything usually found in East Valley of the M-set.

Curiously, increasing the maxiter of today's image has almost no effect.  The low-maxiter hyper stuff in the center has permanently obliterated the higher maxiter stuff that would normally be expected to fill the open area, and raising the maxiter reveals no additional hyper-stuff.

Once again, I have no idea what this new stuff is, but whatever it is, I am becoming more convinced that it is not merely a result of math imprecision.  Hopefully, things will become clearer as I continue the investigation.

The art worth is not all that great, and rates a 7.  The math however is quite interesting, fully worth the rating of 8.5.

The name "Something New" refers to the blueish horn-like feature filling the circular area.  The calculation time of 1-2/3 minutes is well within reason, making the web sites more of a convenience than a necessity.

Cloudless skies and light winds made the temperature of 25F -4C feel almost like spring here at Fractal Central today.  At least the fractal cats thought so, as they lounged in whatever sun they could find on the floor and took turns enjoying the sun on their shelf in the southwest window.  The fractal humans spent the day laughing at the near-hysterical reports from Atlanta, GA, which was brought to a total stop by a little over 2 inches or 6cm of snow, something that would hardly be worth mentioning here in Central Pennsylvania.

The next FOTD will be posted in a day or so.  Many hyper-fractal wonders remain to be discovered, so don't miss it.  Until the time passes, take care, and as I read the current books about cosmology or the quantum, I wonder whatever happened to the days when science was done by observing, theorizing, testing and confirming.  Scientists nowadays seem to have ensconced themselves in an ivory tower, from where they make unprovable pronouncements that they cannot confirm or even understand themselves.

Jim Muth
jimmuth@earthlink.net


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

Something_New      { ; time=0:01:40.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1
  center-mag=+0.254502506168/-0.000471615013/649000/\
  1/47.5/0 params=0/0/0/0/0.997/0/1e-100/0
  float=y maxiter=580 inside=0 periodicity=0
  colors=000cFTdFUdFVdEWeEXeEYeEZfE_fD`fDagDbgDcgDdg\
  DeeGccJbbMa`P__SZYVYXXXnQ1kT3iW4gZ6ea7cd9agAZjBcmD\
  hpEmrGrpHvmJzkKziLzgOzeLzdJzcGzcEwcBtc9uc8re7ph6nk\
  6ln5jq4ht4fqC`nJYhQUdYR`dOYkLWrJUsIQsGNtFKtDHuCEuB\
  BuD8rF7pGAnIFlKKjLPhNTfPXdQ`bSd`TgZNfVSgUWhT_iSdjR\
  hkQllPigMgcKd_IbVF_RDKjwJjvIjuGjtFjsDjrCjqBjp9jo8j\
  n6jm5jl4jkTdWqZHo_Jm_Kl_Lj_Mi_Og_Pe_Qd_Rb_Ta_U__VZ\
  _WUXUQUTMRRHOQDLO9IN1HM5GM9GMDGMHFMKFMOFMSEMWEMZEM\
  bDMfDMjDMmDMnGQnIUnKYnNanPdoRhcUlcWpcYtc_wc`vh`vea\
  vbav_bvWbvTcvQcvNdvKdvGevDevAfv7fv0dz4fv7grBinEjjI\
  lfLmbPoZSpVWrRZsNbuJjzEevG`sHWpJSmKNjMIgNDdP8_O9aQ\
  AcRAdTBfUCgWCiXDjZDl_En`FobFqcGreHtfHuhIwiEznIxjLw\
  fOvcSu_VtXYsTarPdqMgpIkoFnnBsl5qm8onAmoClpEjqHhqJf\
  rLesNctQauS_vUYwYZvWZuVZtUZsTZrSZqRZpQZoPZnO_sJZmN\
  YhQYcTXYWWTZUXhWOaZCXXFWWHVVJUUMTTOSSQRRSRQVQPXPOZ\
  ONaNMcMLeLTu3gRQbGPcFRcFS }

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