Self-organized criticality in self-directing walks

TL;DR

This paper introduces a novel model of self-organized criticality using an operator algebra similar to the Abelian sandpile, analyzing the configuration space and recurrent states.

Contribution

It presents a new self-organized criticality model with an algebraic framework and characterizes its configuration space and recurrent states.

Findings

Defined the structure of the configurational space.

Determined the number of recurrent states.

Proposed an algebraic approach similar to the Abelian sandpile.

Abstract

A new model of self-organized criticality is proposed. An algebra of operators is introduced which is similar to that used for the Abelian sandpile model. The structure of the configurational space is determined and the number of recurrent states is found.