Two par files today illustrating a pecularity of the Zf_Ang formula, one of Paul Carlson's orbit trap formulas.
With a postive "number of iterations to skip" value (imag p2) there is blank space and truncated stalks (which give
some of the orbit trap formulas their name). With a negative imag p2 value the blank space is filled in.
However I have gotten this techique to work only with this one formula. Another quirk of these formulas
is the requirement of using outside=summ to generate high banding count images.
Bypass the calculation process and go to http://maxitersfractalfollies.blogspot.com for immediate viewing
and put the serve back in web server.

fract263.gif       { ; Carlson stalks positive skipped iterations value
                     ; blank
                     ; calctime   0:03:50.63
                     ; created Jun 19, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=frac_ml.frm formulaname=Zf_Ang
  function=sqr center-mag=0/0/0.6666667
  params=-0.2551805169835505/1.054979094821009/3/1/2/128 float=y
  maxiter=1500 inside=0 outside=summ invert=0.5/0/0 cyclerange=0/255
  colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\
  RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\
  9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\
  0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\
  0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\
  0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\
  yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\
  uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\
  o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\
  _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\
  K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007
  }

fract264.gif       { ; Carlson stalks with negative skipped iterations value
                     ; blank
                     ; calctime   0:05:06.60
                     ; created Jun 19, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=frac_ml.frm formulaname=Zf_Ang
  function=sqr center-mag=0/0/0.6666667
  params=-0.2551805169835505/1.054979094821009/3/-1/2/128 float=y
  maxiter=1500 inside=0 outside=summ invert=0.5/0/0 cyclerange=0/255
  colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\
  RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\
  9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\
  0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\
  0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\
  0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\
  yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\
  uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\
  o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\
  _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\
  K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007
  }

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
  ;
}
Roger Alexander

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