2.12 Lambdafn
(type=lambdafn)
Function=[sin|cos|sinh|cosh|exp|log|sqr|...]) is specified with this
type. Prior to version 14, these types were lambdasine, lambdacos,
lambdasinh, lambdacos, and lambdaexp. Where we say "lambdasine" or some
such below, the good reader knows we mean "lambdafn with function=sin".)
These types calculate the Julia set of the formula lambda*fn(Z), for
various values of the function "fn", where lambda and Z are both
complex. Two values, the real and imaginary parts of lambda, should be
given in the "params=" option. For the feathery, nested spirals of
LambdaSines and the frost-on-glass patterns of LambdaCosines, make the
real part = 1, and try values for the imaginary part ranging from 0.1 to
0.4 (hint: values near 0.4 have the best patterns). In these ranges the
Julia set "explodes". For the tongues and blobs of LambdaExponents, try
a real part of 0.379 and an imaginary part of 0.479.
A coprocessor used to be almost mandatory: each LambdaSine/Cosine
iteration calculates a hyperbolic sine, hyperbolic cosine, a sine, and a
cosine (the LambdaExponent iteration "only" requires an exponent, sine,
and cosine operation)! However, Fractint now computes these
transcendental functions with fast integer math. In a few cases the fast
math is less accurate, so we have kept the old slow floating point code.
To use the old code, invoke with the float=yes option, and, if you DON'T
have a coprocessor, go on a LONG vacation!