In this paper we use level set topology optimization to reveal novel phononic crystal topologies which give rise to metamaterial properties including negative and singular effective properties. The level set formalism has been developed on the basis of polynomial functions, the locations of whose zeros control the distribution of material phases. This significantly reduces the number of design variables involved and allows us to search very large design spaces using global optimization techniques. Optimization process reveals that a 2-phase unit cell in which one of the phases is simultaneously lighter and stiffer than the other results in dynamic behavior which has all the attendant characteristics of a locally resonant composite. This behavior is further explored through the use of mode shape analysis. Results presented in this paper are also an example of how purely computational techniques can illuminate novel physical phenomenon.