Comment by ii

If I made a formula that is more generalized, patents still apply?

Here it is in complex numbers:

    p = (r1*cos(ph1 + th) + 1.0*I*r2*sin(ph2 + th))*
   (Abs(cos(m*th/4)/a)**n2 + Abs(sin(m*th/4)/b)**n3)**(-1/n1)

This can produce a number of interesting shapes that original Gielis transforms can't.