Correlated biased random walk with latency in one and two dimensions: Asserting patterned and unpredictable movement

• The balance between irreducible random movement and structured movement is reported for the correlated biased random walk model with latency (CBRWL).
• The CBRWL in two dimensions is constructed from the orthogonal extension of the one dimensional model.
• The relation between drift velocity and tortuosity as a function of entropy density and excess entropy.
• Entropic measures allows to characterize the dynamics independently of the particular control variables.

The correlated biased random walk with latency in one and two dimensions is discussed with regard to the portion of irreducible random movement and structured movement. It is shown how a quantitative analysis can be carried out by using computational mechanics. The stochastic matrix for both dynamics are reported. Latency introduces new states in the finite state machine description of the system in both dimensions, allowing for a full nearest neighbor coordination in the two dimensional case. Complexity analysis is used to characterize the movement, independently of the set of control parameters, making it suitable for the discussion of other random walk models. The complexity map of the system dynamics is reported for the two dimensional case.