We present a theoretical investigation of the emergence of complexity or irreducible information in networked computable systems when the network topology may change over time. For this purpose, we build a network model in which nodes are randomly generated Turing machines that obey a communication protocol of imitation of the fittest neighbor. Then, we show that there are topological conditions that trigger a phase transition in which eventually these networked computable systems begin to produce an unlimited amount of bits of expected emergent algorithmic complexity, creativity and integration as the network size goes to infinity.