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April 15, 1997: Pattern in the Void April 13 April 16 1997 FOTD Home

pattern

Fractal visionaries:

I just drew a couple of those pseudo-true-color, overlapping fractals.  What else can I say but, "Wow! they're great!"  But I still prefer my formulas simple -- the simpler the better. Attached below is a simple Julia formula and par file that takes advantage of the bof60 inside coloring option of Fractint. The few minutes it takes to draw it will be well worth the effort.

I have always been fascinated by the way "real" world patterns keep turning up in various fractals.  I have seen trees, ferns, ice floes, among many other patterns.  But the pattern of the attached fractal is something entirely new, which has no immediate counterpart in the "real" world.  (I enclose "real" in quotes because after 10 years of working with fractals I'm beginning to think like Mr. Pickover, and question exactly what it means to "exist" and "be real".)

The formula itself is a specialized instance of my JulibrotInvZ formula, which I posted previously.  It's curious that as the power of (-Z) gets smaller and the outer shape grow simpler, the interior grows more complex.

My interest in fractals is somewhat specialized. Although I have the means of producing high-definition fractal posters, I don't seem to be able to work up enough interest to exert the effort.  I enjoy the search and discovery aspect of fractal geometry, seeking new twists in old formulas.  The day after I find another "great one", my enthusiasm for that particular fractal has exhausted itself.  I file the image away never to look at it again, and go searching for the next great one.

It's satisfying to know that I'll never run out of places to search.


Jim Muth
jamth@mindspring.com


START FORMULA==================================================

Pattern_in_theVoid { ; time=0:00:36.03-SF5 on P4-2000
  reset=1950 type=formula formulafile=basicer.frm
  formulaname=woven passes=t center-mag=0.29668/0.69\
  1194/2.040883 params=0.64888/1.33663 float=y
  maxiter=90 inside=bof60 logmap=yes periodicity=0
  colors=000noeig_d_V_TPVLJQDEL58SIRYVhYYiXajXdkWgkW\
  jlVnmVqnOFqKOlHXgDfaAoX6xSDpPJgMQ_JXSHcKEiBBp38iIK\
  bWWVjfOxrQpiSh`V`TXTKZLB`D2aJ8cOFdULfZSgdYhicjojkt\
  pahoTYoSblQghPleNpbMuZKzWMt_OmdQghSalUVqWPuTXpRdlP\
  _hMVeKQaIMZGHVDCSB7OUUq_Ab`DYbGTcJOdNIeQDgT8hW3sn5\
  kiBbeHV`NMXTESZLTWRUTYVQcXMjYJpZGw_DpXEiUFbRFWOGOK\
  HHHIAEI3BJGBKUBLfBLsBMeEHTGCPHBLIBGKACLA8M9AQBBTDD\
  XFE`HGdJHgMJkOKoQMsSNvUPzWQwUSsSTpQVlOWiMYeKZbI`ZG\
  aWEcSCdPAfL8gI6iE4jB2jC6jDAiEEiEIiFMiGQhHThIXhJ`hJ\
  dgKhgLlaGmWCnQ7o0VTql2kdBeXJ`QSVI_PAhGFEHCOI9YJ6g7\
  BtC8rG5qe0ba1eZ1gV2jR2lN3nHX7HTDIPJILPJIUJE_KAeK6k\
  IU4IPCJLKJGTKC`K7hCdzEVwGMuICr_IcYGeWEfUChSAjQ8lO6\
  mM4ovugbUlDR5FLHHFTJ9dfUscRs`NrYKrVGqSDqP9pM6pDAvn\
  uKcbVULexcgsZhnViiQjcLlZGmUCnP7o7md9gfAagCWiEQjGKl\
  HEmJ8oZ3DR3X8ZOCOYGDg8bBUNhq`nRnkVojZphbrgfsejtdnu\
  baeQQPED91G9DKAQNAaQAmzv5 }

frm:Woven {; Jim Muth
  z=pixel, c=p1:
    z=(-z)^1.05+c,
      |z| <= 100 }

END PARAMETER FILE==============================================