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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!

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Noel Giffin,