Fractal visionaries and enthusiasts:  

Today's image illustrates what I take to be a bud in the hypercomplex Mandelbrot set.  But the bud is not perfect.  The straight arms converging on the mouth of the bud show that the bud is not a critical one.  In fact, I changed the starting point to 0,0.3,0.3,0 to see what other slices might look like.

I doubt that the hypercomplex set has a single critical point.  The hyperset is actually a four-dimensional hyperslice through the 8-D Julibrot.  But enough of the bud shows through the converging arms to give an idea of the gothic-arch shape of the four-dimensional hypercomplex buds.

I gave the image no rating since almost all its impact is in the mathematical aspect, and its color leaves much that could be improved.  The name "Hyperbud" describes the scene.  The calculation time of 4-3/4 minutes is rather slow.  To avoid delay I recommend viewing the finished image on one of the web sites.

Today here at Fractal Central featured a mix of clouds and sun with a few flurries of snow and a temperature of 39F +4C.  The fractal cat slept through most of it, though he did come to life when tuna and cheddar appeared in his dish.  The humans simply had a human day.

The next FOTD will be posted soon.  Until soon arrives, take care, and I heard on the midday news that if an asteroid were ever to be spotted coming our way, our government would be ready to take action.  The action would be to tell everyone to start praying.

Jim Muth
jimmuth@earthlink.net


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

Hyperbud           { ; time=0:04:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=t
  center-mag=-0.49291912/+0.10220297/268/1/-2.5/0
  params=0/0.3/0.3/0/1.5/0/1e-045/0 float=y
  maxiter=12000 inside=0 logmap=67 periodicity=0
  colors=000R6HR6IR6IR6JR6KS6KS6LT6LT6MU6MU6NV6OW6OX\
  6PY6PZ6Q_6Q`5Ra5Sb5Sc5Td5Te5Uf5Vg5Vh5Wi5Wh5Xh5Xh5Y\
  h5Zh5Zg5_g5_g5`g5ag5af5bf5bf5cf5cf5de5ee5ee5fe5fe5\
  ge5ge6fe6fe6fe7fe7ee7ee8ee8ee8de8de9de9de9deAceAce\
  AceBceBbeBbeBbeCbeCaeCaeDaeDaeDaeD`eE`eE`eE`eF_eF_\
  eF_eG_eGZeGZeGZeHZeHZeHYeIYeIYeIYeIXeJXeJXeJXeKWeK\
  WeKWeLWeLWeLVeLVeMVeMVeMUeNUeNUeNUfOWeNVeNVeNUeNUe\
  NUeNTeNTeNTeNSeNSeNSeNReNReNReNQeMQeMQeMPeMPeMPeMO\
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  zo6zo6zo6zo6zn6zn6zn6zn6z }

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