This research illustrates that complex dynamics of gene products enable the creation of any prescribed cellular differentiation patterns. These complex dynamics can take the form of chaotic, stochastic, or noisy chaotic dynamics. Based on this outcome and previous research, it is established that a generic open chemical reactor can generate an exceptionally large number of different cellular patterns. The mechanism of pattern generation is robust under perturbations and it is based on a combination of Turing’s machines, Turing instability and L. Wolpert’s gradients. These results can help us to explain the formidable adaptive capacities of biochemical systems.