Inherent randomicity in 4-symbolic dynamics

The inherent randomicity in 4-symbolic dynamics will be clarified in this paper. The symbolic sequences bear three characteristics. The distribution of frequency, inter-occurrence times and the alignment of two random sequences are amplified in detail. By using transfer probability of Markov chain (MC), we obtain analytic expressions of generating functions in four probabilities stochastic wander model, which can be applied to all 4-symbolic systems. We hope to offer a symbolic platform that satisfies these stochastic properties and to study some properties of DNA sequences.