Active walker models for complex systems

Many complex systems can be described in a unified way by the simple model of active walker(s). Examples of these complex systems are river formation, movement of heat-seeking missiles, ant swarms, worm movements, polymer reptation, retinal neurons and vessels, electrodeposit and dielectric breakdown patterns, percolation in soft materials, ion transport in glasses, rough surfaces, biological evolution, population dynamics, etc. In an active walker model (AWM), the walker changes the landscape as it walks and its steps are influenced by the changing landscape. In this paper, developments of the AWM are summarized and new results are presented. In particular, the three important areas of application of the AWM-- track patterns, intrinsic abnormal growth, and rough surfaces--are discussed.