Fractal visionaries and enthusiasts:  

The formula behind today's image is Z^(1.09)+C, a hopeless expression if ever there was one.  But as today's image shows, things need not always be as hopeless as it first appears, and an expression as close to linearity as today's can produce interesting fractals when calculated with one of the alternate complex logarithms.

The parent fractal is shaped like a torpedo, much as the minibrot at the center of today's image.  In the range of exponents so close to unity, most all the fractals tend to resemble torpedoes, but this does not mean they are necessarily all the same.  Check the minibrot in today's image, which actually creates a rather pronounced 3-D effect.

Most of this effect is due to my semi-skilled coloring of course, and I rewarded myself with a full half point for the effort.  The name "The Mighty Midget" is a comment on how the image gets so much from so little.  The calculation time of 2-1/2 minutes borders on slowness.  The web sites are there to avoid impatience.

Midsummer arrived with a bang here at Fractal Central today, with a temperature of 86F 30C and an afternoon thunder-shower.  The fractal cat said enough heat is enough and started searching for a cooler spot than the window shelf.  The humans meanwhile had an average day.

The next FOTD will be posted before long, though I'm not sure of the route.  Until whenever and however, take care, and be ever aware of the dangers inherent in making hasty decisions that will do nothing but make someone feel better.

Jim Muth
jimmuth@earthlink.net


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

The_Mighty_Midget  { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-0.192308145885724/-1.991515836863857/\
  2998.507/1/57.5/0 params=1.09/0/525/0 float=y
  maxiter=5000 inside=0 logmap=140 periodicity=6
  colors=00060F70F70F80F90F90FA0FA0EB0EC0DC0DD0DD0EE\
  0EF0FF0EG0DG0BH09I08I06J14J03K14K24K34L44L54L64M74\
  M84M94NA4NB4NC5ND5OE5OF5OG5PH5PI5PJ5QK5QL5QM5QN5RO\
  6RP6RQ6SR6SS6ST6TU6TV6TW6UX6UY6UZ7U_7V`7Va7Vb7Wc7W\
  d7We7Xf7Xg7Xh7bn7_k7Xh7Ve7Sb7Q_7NX7KU7IR7FO7DL7AI7\
  7H58G68G78G78G88G98G98GA8GB8GB8GC8GD8GD8GE8GF8GF8G\
  G8GG8FH8FI8FI8FJ8FK8FK8FL8FM8FM8FN8FO8FO8FP8FQ8FQ8\
  FR8FR8ES8ET8Qh8Qg8Qf8Qe8Qd7Qc7Qb7Qa7Q`5UeN6SQBWTGZ\
  VLaYQe`Vhd`mbZkaXj_VhZTgXReWPdVOcTMaSK`QIZPGYNEWMC\
  VN9WLBUKDSJEQIGPGINFJLELKDMIBOGAQF9RD8Tz6Vz5Wz4cz4\
  `z3cz3Xz3cz3Uz3cz3Uz2cz2Uz2cz2Uz2czUUzUUzUUzUUzUcz\
  UczUczUczUczUczUczUczUczUczUczUczc_kcbjceichhckgcn\
  fclecjechecfecdeccecceccecceccecczcczcczcczcczcczc\
  czcczcczmmzmmzmmzmmzmmzmmzmmzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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