Technical data for this type of fractal : click here.

For the fractal here :
fn1 = tan(), fn2 = sqr(), fn3 = tan(), fn4 = asinh()
real(p1) = 4, imag(p1) = 4, real(p2) = -10, imag(p2) = 0, real(p3) = 6, imag(p3) = -6

Note :
If real(p1) = 2 instead of 4, the aspect of the fracttal becomes :