I read about so called "wild" automorphisms of the field of complex numbers (i.e. not the identity nor the complex conjugation). I suppose they must be rather weird and I wonder whether someone could explain *in the simplest possible way (please)* how I could imagine such wild automorphisms.

E.g. I suppose they are completely discontinuous.
E.g. are the real rational numbers fixed or any other set of complex numbers?
Can such an automorphism be pictured in a model?