In the following picture, you see the identity map on the complex
plane,
the filled Julia set for F(z) = z^2 + 0.25 (with some orbits
converging to 1 highlighted),
and the basins of attraction for the
Newton's method applied to G(z) = z^3 - 1.
In the following picture, you see the approximation to the Julia set
for H(z) = z^2 + i,
obtained by the method of inverse iteration.