General Functions

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General Functions Support

This section describes a set of general functions available to your Fractal Science Kit fractal programs.

Sigmoid(z) = 1/(1+Exp(-z))
Logit(z) = Log(z/(1-z))
Expm1(z) = Exp(z)-1
Log1p(z) = Log(1+z)
Bifurcate(z) = z*(1-z)
Cardiod(z) = z+0.5*z^2
Convex(z) = z/(1-z)
Cayley(z) = (z-1i)/(z+1i)
Poisson(z) = (1+z)/(1-z)
Airfoil(z) = z + 1/z
Airfoil2(z) = z - 1/z
Bipole(z) = 1/(z+1) + 1/(z-1)
Dipole(z) = 1/(z+1) - 1/(z-1)
Gudermannian(z) = 2*Atan(Exp(z)) - 0.5*Math.PI
AGudermannian(z) = Log(Tan(0.25*Math.PI + 0.5*z))
Catenary(z,a) = IIf(a=0, 0, a*Cosh(z/a))
Pursuit(z,a) = a*z^2 - Log(z)
CircleInvolute(t,a) = Complex(a*(Cos(t) + t*Sin(t)), a*(Sin(t) - t*Cos(t)))

 

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