The behaviour of King's Dream is such amazing. There are any modifications with the initial values (X0 and Y0) but with the number of iteration and mostly with the constant values. Indeed, a small difference ( 10 %) gives different figures.
    This fractal is perhaps very simple but its study is very interesant. I think we can develop such a study.

    Moreover, this kind of work is very interesant because we can choose our own subject even if there is still a theme : Hydrodynamic Instabilities.