; May 26, 1997: Land of Loti 
;
; loti
;
; Fractal visionaries:
;
; Today's fractal picture is a gentle yet striking one created by doing
; things a little differently with Newton's method.  I've named it Lotus
; because it reminds me of a patch of lotus blossoms.
;
; As a rule, I find the Newton's formulas quite productive, since there is
; no end to the different ways they can be calculated, and the results are
; always unpredictable.  Certain terms in these formulas are unusually
; sensitive, and if they are changed even slightly, the entire appearance
; of the resulting fractal will be changed.  Even when the parameters are
; so far off that a blank screen results, an interesting image can usually
; be found by trying various fill options.
;
; Adding variable parameters to simple formulas is one of my favorite ways
; of finding new images in my test formulas.  Instead of writing say,
; (Z*(Z-1))^2, I might write X*((Z*(Z-Y))^W), which gives me the three
; variables, X, Y, and W to play with.
;
; One problem with having 10 variables, as I sometimes do though, is that
; when I find a good fractal, if I don't make an immediate record of the
; parameters, I lose the fractal and never find it again.  When I find
; values that work particularly well, I make them a hard coded part of the
; formula and thereby eliminate many of the variables.
;
; I've seen remarks recently that Fractint can't recognize the color part
; of the parameter files.  This is most likely because the the color code
; is being broken up into fragmentary lines by the online software.  To
; avoid the problem, be sure that the parameter file is saved as ascii
; text, and that every line in the color section of the parameter file
; ends with a backslash < \ >.  This indicates to Fractint that the next
; line is a direct continuation of the previous line.
;
; Tomorrow's fractal will be a cosmically grand one, also created by a
; variation of Newton's method.
;
; Jim Muth
; jamth@mindspring.com
;
; START PARAMETER FILE FOR 19.6===================================

Land_of_Loti       { ; time=0:00:33.18-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=NewtonTest27 passes=1
  center-mag=1.4623/0/0.3582555/1/-90/0
  params=-1/3/3/1/1/1e-005 float=y maxiter=90
  inside=bof60 logmap=yes periodicity=0
  colors=000hKmhKjhKghKdlR_pYVtdQxkMH1tIEvK0pK0oOArS\
  IrWPr_XrccrgkzzzzrrreljcjX`gPZeIWbBU`4QWHMRTIMeFIq\
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  YcbQfX4eY5eY6eY7eZ7`QlhLq
}

frm:NewtonTest27 {; Jim Muth
  a=real(p1), b=imag(p1), c=real(p2),
  d=imag(p2), k=real(p3), f=imag(p3),
  z=(pixel):
  zx=(z^b)-a
  zy=(c*z)^d
  z=z-(k*zx/zy),
  |zx| >= f
}

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