Abstract
Deterministic walks over a random set of points in one and two dimensions ( ) are considered. Points (“cities”) are randomly scattered in following a uniform distribution. A walker (“tourist”), at each time step, goes to the nearest neighbor city that has not been visited in the past steps. Each initial city leads to a different trajectory composed of a transient part and a final -cycle attractor. Transient times (for ) follow an exponential law with a -dependent decay time but the density of cycles can be approximately described by . For and , the exponent is independent of . Some analytical results are given for the case.
- Received 5 May 2000
DOI:https://doi.org/10.1103/PhysRevLett.87.010603
©2001 American Physical Society