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\
  MOgSUZY_PcdG_aEW_CSYAPW8LT6HR4DP2AN0DhzGetIcsKakN_\
  lPYmRWnYTpcQqjNrpKsvItz_Wmp8zo2sn7mnCdnHVmMKmRDmW6\
  m`JbgVTmfIsr8yJNmQP3NUBKZJHcREgYBle8qm6utBslFreKqZ\
  OoRTnKXmDVkCUiCThBSfBQdBPcAOaAN`ALb9Jd8If7Gh6Ej5Dl\
  4Bn3Ap2Ii4Pc6WY8cRAjLCqFErEDsECqFDoGEmHFkHGiIHgJIe\
  KJdKKbLL`MMZNNXNOVOPTPQRQRQQS_ObhNlgOjgPhgQgabIfRe\
  fScfTbeT`eUZeVYdWWdXVdYTcYRcZQc_Ob`MbaLbbJ52oA7jEC\
  fIGbMLZRQUVUQZZM7aoFbfNbZVbQr0Aq3Bp5Bo8CnACmDDlFDk\
  IEjKEiMFhPFgRGfUGeWHdZHc`I2t37r5Bp7Fn8JlANjCRhDVfF\
  ZdHUYpVZnVZlWZkWZiX_gX_fX_dY_bY`aZ`_Z`Y_`X_aV_aT`a\
  S`aQabOabNbbLbbJ6HaCLYHPVNSSSWOY_L5`_7aZ9aYBaXDaWE\
  aVGaUIaTKaSMaRNbQPbPRbOTbNVbMWbLYbK_bJabIwryuqvtps\
  sopqnnpmkolhmkeljcki`ihYhgVgfTeeQddNccKiewgdnfcfdc\
  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=====================================