
manowar

      c = z1(0) = z(0) = pixel
      z(n+1) = z(n)^2 + z1(n) + c
      z1(n+1) = z(n)
    Parameters: real & imaginary perturbations of z(0)


Two of Fractint's faithful users went bonkers when we introduced the
"formula" type, and came up with all kinds of variations on escape-time
fractals using trig functions. We decided to put them in as regular
types, but there were just too many! So we defined the types with variable
functions and let you, the, overwhelmed user, specify what the functions
should be! Thus Scott Taylor's "z = sin(z) + z^2" formula type is now the
"fn+fn" regular type, and EITHER function can be one of sin, cos, tan, cotan,
sinh, cosh, tanh, cotanh, exp, log, sqr, recip, ident, conj, flip, or cosxx.

Plus we give you 4 parameters to set, the complex coefficients of the two
functions! Thus the innocent-looking "fn+fn" type is really 256 different
types in disguise, not counting the damage done by the parameters!

Some functions that require further explanation:

 conj()   - returns the complex conjugate of the argument. That is, changes
            sign of the imaginary component of argument: (x,y) becomes (x,-y)

 ident()  - identity function. Leaves the value of the argument unchanged,
            acting like a "z" term in a formula.

 flip()   - Swap the real and imaginary components of the complex number.
            e.g. (4,5) would become (5,4)

Lee informs us that you should not judge fractals by their "outer"
appearance. For example, the images produced by z = sin(z) + z^2 and
z = sin(z) - z^2 look very similar, but are different when you zoom in.

