Fractal visionaries:

Every so often I discover something entirely new and completely unexpected in the mandeloid family.  Today's image is one of those discoveries.  It's actually part of the order 2.0029 julibrot figure, sliced in a direction slightly removed from the Julia planes in the area of the East valley of the prominent negative X-axis midget.

At a power of 2.0029, the midget has just begun to split apart, revealing lots of interesting new stuff to explore, both at the positive and negative ends.  When I went to the Julia set of the positive end of the midget, I suspected that something unusual might lie there, but I never expected the crazy square spirals that appeared when I turned slightly from the Julia direction.

These unusual square-spiral objects are extremely localized inside a sharp-edged rectangular box, the edge of which exists just beyond the borders of today's picture.  This little rectangular area just outside today's image may be the most incongruous I've yet found.

One more point of curiosity -- the image makes the largest 640x480 gif file I've yet saved -- over 360kb.  The fractal is a rather slow one, so it might be advisable to pick it up from a.b.p.f. or a.f.p. where it has been posted.

For tomorrow -- who knows -- I might do further exploring in this crazy area I've just run into.  There's only one way to be sure -- wait and see.


Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

Angular_Iterations { ; time=0:01:46.06-SF5 on P4-2000
  reset=1960 type=formula formulafile=jul-97.par
  formulaname=JulibrotZpwr passes=1
  center-mag=-0.00019376290852973/+0.072384826150150\
  07/745.861/1/17.5/0 params=2.0029/0/-1.7438/0/0.00\
  13/0.0013 float=y maxiter=1200 inside=bof60
  logmap=yes periodicity=10
  colors=000C_6C_6C_6C_6C`6C`6C`6C`6C`6C`6C`6Ca6Ca6C\
  a6Ca6Ca6Ca6Ca6Cb6Cb6Db6Db6Db6Db6Db6Dc6Dc6Dc6Dc6Dc6\
  Dc6Dd6Dd6Dd6Dd6Dd6Dd6Dd6De6De6De6De6De6De6De6Df6Df\
  6Df6Df6Df6Df6Df6Dg6Dg6Dg6Dg6Dg6Dg6Dg6Eh6Eh6Eh6Eh6E\
  h6Eh6Eh6Ei6Ei6Ei6Ei6Ei6Ei6Ei6Ej6Ej6Ej6Ej6Ej6Ej6Ej6\
  Ek6Ek6Ek6Ek6Ek6Ek6Ek6El6El6El6El6El6El6Em6Em6Em6Em\
  6Em6Fm6Fm6Fn6Fn6Fn6Fn6Fn6Fn6Fn6Fo6Fo6Fo6Fo6Fo6Fo6F\
  o6Fp6Up6Up6Up6Up6Up7Up7Up8Up8Up9Uq9cqAcqAcqBcqBcqB\
  cqCcqCcrDcrDcrEcrEcrFcrFcrFcrGcrGcsHcsHcsIcsImsIms\
  JmsJmsKmsKmtLmtLmtMmtMmtMmtNmtNmtOmuOmuPmuPmuQmuQm\
  rRAoTClUFiVHfXKcYM`ZPY`RVaUTbWQcZNe`KfcHgeEihBjj8k\
  m5mo2no2nn3mn3mm3lm3ll4kl4kk4jk5jj5ij5ii5hi6hh6gh6\
  gg7fg7ff7ef7ee8de8dd8cd9cc9bc9bc9bbAabAaaA`aB``B_`\
  B__BZ_CZZCYZCYYDXYDXXDWXEWWEVWEVVEUVFUUFTUFTTGSTGS\
  TGSSGRSHRRHQRHQQIPQIPPIOPIOOJNOJNNJMNKMMKLMKLLKKLL\
  KKLJKLJJMIJMIIMHIMHHNGHNG }

frm:JulibrotZpwr {; Jim Muth
; Draws oblique XY-ZW slices of order n Julibrot Figure
; P1 defines power of Z, P2 sets center of slice
; P3 sets angle of slice
 z=pixel, c=p2+(pixel*p3):
  z=z^p1+c,
   |z| <= 100 }

END 19.6 FILE===============================================