Precondition
Be sure to know the basic math: Math HomeIntroduction: Identity Functions
If h(x) with inverse hInv(x) is a bijective function (one-to-one), define the identity function I(x) = hInv( h(x) ).Because hInv is the inverse of h: I(x) = hInv(h(x)) = x; I(x) = x.
Examples for Identity Functions I(x)
- I(x) = a(x) = sqrt(x*x)
- I(x) = a5(x) = pow(pow(x,5),1/5)
- I(x) = log(exp(x)) = iExp(x)
- I(x) = asin(sin(x)) = iSin(x)
- I(x) = acosh(cosh(x)) = iCosh(x)
Identity Functions Extended and Fractals
E.g. the generation function for the nova set is nova(z,c) = z + 1/z + c.Generated is a sequence dependent on z, with a "disturbing parameter" c.
Transforming nova(z,c) with an extended identity function I(x,constant,c):
hInv(h(nova(z,c) + constant)) + c