Phase transition is controlled by controlling fractal dimension of a fractal-coupled structure overall or locally. For a magnetic material, ferromagnetic phase transition temperature of magnetic particles arranged to have self-similarity is controlled by fractal dimension. For a half-filled electron system confined in a treelike fractal, Mott transition is controlled by fractal dimension of the system. Stronger quantum chaos than conventional ones is generated by adding magnetic impurities to the fractal-coupled structure, and through this process, Anderson transition is controlled.