Fractal visionaries and enthusiasts:

There are minibrots and there are more minibrots, and then there are things like the minibrot in today's image.  I'm not sure if it's a minibrot or not.  If either or both real(p3) and real(p4) are changed to zero, the image becomes just another scene not too deep in Seahorse Valley of the Mandelbrot set, but when real(p3) is set to 0.77 and real(p4) is set to the reciprocal of one-googol, the minibrot fills with totally new stuff, which can be zoomed into and explored, and therefore is not an artifact.

The formula draws the hypercomplex Mandelbrot set, and it does so quite well.  But how is it possible that a value as infinitesimal as the 10^-100 of real(p4) can make such a difference in the image?

Regardless of how the image came about however, a whole new world lies inside the minibrot, waiting to be explored.  I'll do a little exploration in tomorrow's FOTD, but I really want to get that FOTD web-site logo finished.

The rating of an 8 is based on the mathematical interest.  The artistic value of the image is everyday average.  The calculation time of 1-1/4 minutes will cause no pain to any fractal fanatic.

Nondescript weather prevailed here at Fractal Central on Tuesday.  This means partly cloudy skies and a temperature of a humid 84F 29C.  The fractal cats ignored the outside conditions and clung to the cool air most of the day.  In my department the work was busy, but thanks to FL, it was finished without a hitch.  Unfortunately however, due to the rush, the FOTD web site logo remains in the rudimentary stage.

The next FOTD will be posted in 24 hours.  Until then, take care, and I hear that Australia recently recorded the lowest temperature in that nation's history.  This could mean that all the fuss about global warming has been a false alarm, but more likely, we're confusing weather with climate.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

Whole_New_World    { ; time=0:01:16.34-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1
  center-mag=-0.7583459371/+0.0768359714/28534.27/1/\
  34/0 params=0/0/0/0/0.77/0/1e-100/0 float=y
  maxiter=875 inside=0 logmap=-109 periodicity=0
  colors=000OJiOJkOJlOJnOJoOJmOJkPJjQJhRJfSJeTJcUJaV\
  J`XJZZJX`JWbJUdJSfJRhJPjJNkJMjLOiNPhPRfRSeTUdVVbXW\
  aZY``ZZb`YcaXecVgdUieTkgRmhQojPqkNsmMtnLuoJslIqiHo\
  fGlcFj`EhYHeXKbWM_VPXURTTURSWPRZOQ`OQbOQdPQfQQgRQi\
  SQkTQmVQnWQpXQrYQtZQu_Qt`Tt`WsaZsaasbcrbfrciqclqdo\
  qdqpeppfpogpohpoipnjpnkpnkpmlpmmplnploplppkqpkrpkr\
  pjspjtpiupivpiwphxphyphypeuncrlaoj_lhXifVfdTccR`aO\
  Y_MVYKRWIOUFLS10HDIRBFP9CN69L46J23HCUNBRMAPL9NL8KK\
  7IK6GJ5DJ4BI39I26H14H02G2nE1kF1hF1eF1cF1`F1YF1WF1T\
  F1QF0OG0LG0IG0GG0DG0AG08G05G02G3g92bA2ZB2UC1QC1MD1\
  HE0DE08F04GP`ZNYXMWWKUVJSUHQTGNSELRDJQBHOAFN8DM7AL\
  58K46J24I12HLjJKhIJfIIdIHbIG`IFZIEXIEVIDTHCRHBPHAN\
  H9LH8JH7HH7FH6DG5BG49G37G25G13G01GIBWGAUF9TD8SC7QA\
  6P95O74M63L42K31I10HzzBvzCrcCzmChPCcODZMDULDPJDKIE\
  AGE0FENzHOzIOzJPzKznMzmNzlOzjczihzgmzfrzdvzjzzmzzm\
  zzmzzrzzvzzzzzzzzzzzzzzzz }

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