Fractal sets attached to homogeneous quadratic maps in two variables

► Fractal sets attached to “generic” homogeneous quadratic maps are studied. ► Using invariant theory, two invariants give rise to only six “normal forms”. ► Normal forms partition the plane of invariants into eleven connected regions. ► Comparison of “topological types” for pairs of fractals, per region. ► Conjecture: only a finite and small number of distinct topological types exist.