Fractal visionaries and enthusiasts:  

Today's image highlights one of the mystery buds of the 4-D HyperMandelbrot set.  But the mystery bud is not the reason I posted the image.  The most striking part of the scene is the fine display of moire patterns filling the bud.  And this pattern will change with every change, however small, of overall image size, resolution or magnitude.

0+0i is the critical starting point of the 2-D Mandelbrot set, so I assume 0+0i+0j+0k would be the critical starting point of the 4-D HyperMandelbrot set.  At the same time, I have no idea what the perturbed Hyper-sets might look like.  Today's scene might be critical, it might be perturbed.  One thing for sure is that much more exploration needs to be done.

The name "Patterns in a Void" refers to the Moire patterns filling the open area of the bud.

The math interest rates a very respectable 8, the artistic value however is worth no more than a humdrum 6.  I leave it to the individual fractalist to decide whether the image is worth the quarter hour required to calculate it.  If the decision is negative, the web sites are there to bring relief.

Heavy clouds, (stratocumulus for the weather-wise), prevailed all day yesterday and today here at Fractal Central, though no rain fell.  Because of the high humidity, the temperature of 66F 19C felt just about right.  The fractal cat had an active day, often dashing up and down the hallway as though chasing or being chased by an invisible cat.  The humans had a slow day, which is boring to read about but was relaxing to experience.

The next FOTD will be posted soon.  Until soon arrives, take care, and in June 1976 I spent two days in Seattle.  On both days the weather was sunny and quite warm, proving that despite its reputation of being a cloudy and rainy city, Seattle is a sunny and warm city.

Jim Muth
jimmuth@earthlink.net


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

Patterns_in_a_Void { ; time=0:15:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1 float=y
  center-mag=-0.010735/0.113631/41 maxiter=12000
  params=0/0/0/0/0/11/1e-111/1e-111 inside=0
  logmap=-590 periodicity=0
  colors=000r6Sr6Sr6Sr6Tr6Tr6Tq6Tr6Us6Us6Ut6Uu6Uv6Vv\
  6Vw6Vx6Vx6Vw7Uw7Uv8Uv8Tv8Tu9Tu9SuAStAStARtBRsBRsBQ\
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  OGgPFgPFfQFfQEfQEeREeRDeRDdSDdSDdTCcTCcTCcUBbUBbVB\
  bVAaVAaWAaW9`W9`X9`X8_Y8_Y8_Y7ZZ7ZZ7ZZ7__8__9__9_`\
  A_`A_`B_`B_aC`aC`aD`aD`bE`bE`bF`cF`cGacGacHadHadIa\
  dJadJaeKaeKbeLbeLbfMbfMbfNbgNbgObgOcgPchPchQchQchR\
  ciRciSciTdiTdjUdjUdjVdkVdkWdkWdkXelXelYelYelZemZem\
  _em_en`fn`fnafnbfobfocfocfodfpdgpegpegpfgqfgqggqgg\
  rhgrhhrihrihsjhsjhskhslhtlhtmitmitniuniuoiuoivpivp\
  ivqjvqjwrjwrjwsjwsjxtjxtjxulzvkyukzujzvjzwjzxizyiz\
  zizzhzzhzzhzzgzzgzzgzzfzzfzzfzzezzezzezzdzzdzzdzzc\
  zzczzczzbzzbzzbzzazzazzazz`zz`zz`zz_zz_zz_zzZzzZzz\
  ZzzYzzYzzYzzXzzXzzXzzWzzWzzWzzVzzVzzVzzUzzUzzTzzTz\
  zTzzSzzSzzSzzRzzRzzRzzQzz }

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