Antideterministic Sequence

An antideterministic sequence is a sequence generated by selecting new terms to discourage repetitions of earlier blocks (Urbanowicz et al. 2005). One construction starts with terms , ..., in the closed interval and integers and , with . For a candidate new term , define the block distance

(1)

where or, with the interval endpoints identified, . The utility function is

(2)

and the next term is chosen to satisfy

(3)

For , this maximizes the distance from the new block to its nearest earlier block. The maximum exists by continuity on the closed interval . Choosing the least maximizing argument resolves ties and makes the rule deterministic once the seed is fixed. Some seeds can make identically zero, so the rule alone does not guarantee nonperiodic behavior.

The construction aims to suppress close parallel diagonal patterns in a recurrence plot. The periodic-distance version is used by Trott (2006).