Fractal visionaries:

Since it is a weekend everywhere and a holiday weekend in the USA, not many will be sitting in front of their computers when there's so much more to do outdoors.  But for those who spend holidays inside searching for fractals, here's a striking one.

A week or so ago I saw a message on sci.fractals, (I believe it was from Jon), asking if anyone had done much work with Z^Z and Z^(-Z) formulas.  I have done a bit of work with this type of formula.  In fact I've made exponent towers of various combinations of ^Z and ^(-Z) up to 12 levels high.

The resulting images are always filled with discontinuities and fragments of various shapes.  Often they are too chaotic, with no center of attention, but sometimes the fragments join together into a pretty good picture.  Today's fractal is one of those good ones, where the floating fragments and big blocky squares make a reasonable picture.

Today's formula is loaded with possibilities.  With all the variables to play with, one could spend a lifetime and not see > all that this formula has in it.  And I've got a couple dozen variations on file.

For tomorrow, I've got a most unusual Newton image waiting.

Jim Muth
jamth@mindspring.com


START PARAMETER FILE FOR 19.6===================================

Squarely_Within    { ; time=0:00:39.27-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=TowerMinExp04a function=sin/sqr/sinh/\
  sinh passes=1 center-mag=-0.9074/0/0.144573/1/-90\
  /0 params=1.5/0/0.333/0/0.8/0 float=y maxiter=500
  inside=bof60 logmap=yes periodicity=10
  colors=000DBFIQPNLNNLMNLMNKLNKKNKKNKJNJJNJINJHNKHN\
  JGNIFNIFMIEMIEMHDMHCMHCMHBMHAMGAMG9MG9MG8MF7MF7MF6\
  MF6NE7OE7OE8PE8PE8QE9RE9RE9SEASEATEATEBUEBVEBVECWE\
  CWECXEDYEDYEDZEEZEE_EE_EF`EFaEFaEGbDGbDHcDHdDHdDIe\
  DIeDIfDJfDJgDJhDKhDKiDKiDLjDLkDLkDMlDMlDMmDNmDNnDN\
  oDOoDOpDOpEPqGPqIPpKQpMRpORpQSpSSpUToWUoYUo_VoaWoc\
  WoeXogXoiYokZomZon_oo`np`nqanransbntcnucnvdnwdnwen\
  wfnwfmwgmwhmwhmwimwimwjmwjlwklwklwkkwlkwljwljwliwm\
  iwmhwmhwmgwngwnfwnfwnewoewodwodwocwpcwpbwpbwpawqaw\
  q`wq`wr`wr_wr_wrZwsZwsYwsYwsXwtXwtWwtWwtVwuVwuUwuU\
  wuTwvTwvSwvSwvRwwRwwQwwQwwPwxPwyPxzOyzOzzOzzNyzNyz\
  NyzNyzMxzMxzMxzMxzLwzLwzLwzLwzKwzKvzKvzKvzJvzJuzJu\
  zJuzIuzItzItzItzHtzHtzHszHszGszGszGrzGrzFrzFrzFqzF\
  qzEqzEqzEpzEpzDpzDpzDpzDozCozCozCozCnzBnzBnzBnzBmz\
  AmzAmzAmzBlzBkzCkzCjzCjzDizDhzDhzEgzEfzEfzFezFezFd\
  zGczGczGbzHazHazH`zI`zI_z }

frm:TowerMinExp04a {; Jim Muth
z=pixel, c=p2+(p3*pixel):
z=z^fn1(z^fn2(-z^fn3(z^fn4(-z+p1))))+c,
|z| <= 100 }

END PARAMETER FILE FOR 19.6=====================================