Fractal visionaries:

Today's fractal looks like a burgundy bullet caught by a stop-action camera.  Even the shock wave is visible, so I named it "Bullet".  Actually, it's a midget in the XW plane, where everything resembles a parabola with the open end in the positive direction.  Don't let the maxiter of 3,000,000 worry you; all the open areas are periodic, and the picture draws in under 2 minutes.

The picture raises an interesting question -- what feature is to be considered the entire midget -- the bullet-shaped central area, or the vertical band partially obscured yet still clearly visible through the parabolic chaos?  This band must be part of the midget because it forms part of the midget's boundary.

The breaks in the overlying chaos, where this dark band shows through, represent all the perturbed Mandelbrot sets with purely imaginary starting points, where parts of this particular midget are visible.  Here again, we have an example of the totally different behavior of the low and high iteration parts of the fractal.  This different behavior demonstrates that regardless of where a point starts, if it doesn't escape first, it will eventually settle into the same orbit as a point that started at 0,0.

And right now, I'm going to settle into my favorite chair to watch the evening news on TV.  Today's finished product has been posted to a.b.p.f. and a.f.p. as always.  For tomorrow -- I don't know.  We'll see when the time comes.

Jim Muth
jamth@mindspring.com


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

Bullet             { ; time=0:00:13.40-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=XY-XWrotation passes=1
  center-mag=-0.00594679/0/3.26976/5.4395
  params=89.99/0/0/0/-1.7545/0 float=y
  maxiter=3000000 inside=0 logmap=yes periodicity=10
  colors=000OFFNFELFCKFBIE9HE8FE6DE5AF3CF4DE5FE6HE7I\
  E8KD9MDANDBPDCRCDSCEUCFWCGXBHZBI_BJaAKcALdAMfANh9O\
  i9Pk9Qm9Rn8Sp8Tr8Uv3Qs7TqCXnG_kKbiPffTicXl``oZesWi\
  vXiuXhuYhtZgs_gr_fr`fqafpaepbeocdnddmdcmeclfbkgbkg\
  bjhaiiahi`hj`gk_fl_el_emZdnZcnYcoYbpXaqX`qW`rW_sWZ\
  vU_tVZqXYoYYlZXj`WgaVebUbcT`eTYfSWgRTiQRjPOkOMmOJn\
  NHoMEpLCrK9sJ7tJ4vI2wH2vI3tJ3sK3qL3pM4nN4mN4kO5jP5\
  hQ5gR5eS6dT6bU6aV6_W7ZX7XY7WY8UZ8T_8R`8Qa9Ob9Nc9Mc\
  8Lb8La8K`7K_7KZ7JY7JX7JW7JW6IV6IU6IT6HS6HR6HQ5GP5G\
  O5GN5FM5FL5FK4EJ4EJ4EI4EH4DG4DF3DE3CD3CC2BB3CC3CD4\
  CE4CF4CF4CG5CH5CI5DJ6DK6DK6DL6DM7DN7DO7DP7DP8DQ8DR\
  8DS9DT9DU9EU9EVAEWAEXAEYBEZBEZBE_BE`CEaCEbCEcCEcDE\
  dDFeDFfEFgEFhEFhEFiFFjFFkFFlEElFFlFFlGGlHHlHHlIIlI\
  JlJJlKKlKLlLLlMMlMNlNNlNOlOPlPPlPQlQQlRRlRSlSSlSTl\
  TUlUUlUVlVWlWWlWXlXYlXYlYZlZ_lZ_l_`lAPC8PA7P98OAbI\
  T`IS_IQYHPXHNVHMTHKSGJQGH }

frm:XY-XWrotation {; Jim Muth, thanks to Benno Schmid
; p1 = rotation angle in degrees, p2 = parallel planes
; p3 = point of rotation and parallel planes
z=sin(p1*.01745329251994)*flip(imag(pixel))+p2,
c=cos(p1*.01745329251994)*flip(imag(pixel))+real(pixel)+p3:
z=sqr(z)+c
|z| <= 16 }

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