Patterns with 12- fold rotational symmetry is observed in soft matter systems like liquid crystals, block copolymers, miscelles, surfactants etc.  If we rotate these patterns by 360/12 degrees, you will find exactly the same pattern as the original. Usually, these are found as a combination of squares and triangles. Here applying a specific soft matter system, I obtained curved squares and triangles as entropically favorable structures. Thus with the physics-induced matching rules, we have a beautiful set of tiles that can be arranged to aperiodic tilings.

A huge acknowledgment goes to Dr. Petra Staynova who is sporty enough to cut these pieces upon an impulsive request.