Today's fractal is yesterdays posting reprised.The Carlson stalk formulas are  great examples
 of programming ingenuity. Clever algorithmic insight takes Fractint, which is essentially
 a 2 dimensional plotting program, and produces convincing pseudo-3d images.
Ready made at http://maxitersfractalfollies.blogspot.com

fract393.gif       { ; Carlson stalks
                     ; blank
                     ; calctime   0:21:01.79
                     ; created Aug 30, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=frac_ml.frm formulaname=Zf_Ang
  function=cotan center-mag=0.0112924/0.0250417/2.73224
  params=0.5/0.5/0.5/-12/2/128 float=y maxiter=1500 inside=0
  outside=summ
  colors=000zzzzyyzxxzwwzvvzuuzttzsszsszrrzqqzppzooznnzmmzllzkkzkkzjjziizh\
  hzggzffzeezddzcczcczbbzaaz``z__zZZzYYzXXzWWzWWzVVzUUzTTzSSzRRzQQzPPzOOzO\
  OzNNzMMzLLzKKzJJzIIzHHzGGzGGzFFzEEzDDzCCzBBzAAz99z88z88z77z66z55z44z33z2\
  2z11z00y00x00w00v00u00t00s00r00q00o00n00m00l00k00j00i00h00g00e00d00c00b0\
  0a00`00_00Z00Y00W00V00U00T00S00R00Q00P00O00N00L00K00J00I00H00G00F00E00D0\
  0B00A00900800700600500400300100000yyzxxzwwzvvzuuzttzrrzqqzppzooznnzmmzll\
  zjjziizhhzggzffzeezddzbbzaaz``z__zZZzYYzXXzVVzUUzTTzSSzRRzQQzPPzNNzMMzLL\
  zKKzJJzIIzHHzFFzEEzDDzCCzBBzAAz99z77z66z55z44z33z22z00z00z00y00x00w00v00\
  u00t00t00s00r00q00p00o00n00n00m00l00k00j00i00h00h00g00f00e00d00c00b00b00\
  a00`00_00Z00Y00X00W00W00V00U00T00S00R00Q00Q00P00O00N00M00L00K00K00J00I00\
  H00G00F00E00E00D00C00B00A009008008007006005004003002001
  }
frm:Zf_Ang {; Copyright (c) Paul W. Carlson, 1998
    ; p1       = Julia set coordinates
    ; real(p2) = controls size of the elements
    ; imag(p2) = number of iterations to skip
    ; real(p3) = number of color ranges
    ; imag(p3) = number of colors in a range
    ;
  z = k = iter = range_num = bailout = 0
  w = pixel
  c = p1
  prev_modw2 = 1.0e20
  size = real(p2)
  skip_iters = imag(p2)
  num_ranges = real(p3)
  colors_in_range = imag(p3)
  factor = (colors_in_range - 1) / size
  :
  w = c * (w - 1 / w)
  a = 2 * atan(imag(w) / real(w))
  a = a * a + c
  a = fn1(1 - a) / a
    ;
  dist = abs(|w| - |a|)
  IF (dist < size)
    bailout = 1
    IF (iter > skip_iters)
      k = 1
    ENDIF
    z = (factor * dist + range_num * colors_in_range + 1) * k
  ENDIF
  range_num = range_num + 1
  IF (range_num == num_ranges)
    range_num = 0
  ENDIF
  iter = iter + 1
  z = z - iter
  bailout == 0 && |w| < 1.0e20
  ;SOURCE: 98msg.frm
}
Roger Alexander