These animations represent the evolution of iterated function systems with hyperbolic symmetry from one symmetry type to another. The first has radically different symmetry types, while the second swaps the "missing" reflection (all the reflections are visible in its middle frame).

[3+,7] to [8,5] hyperbolic symmetry

[4+,6] to [4,6] to [4,6]+ hyperbolic symmetry