Framework of two-dimensional functional walks

TL;DR

This paper introduces the concept of two-dimensional functional walks, detailing their notation, definitions, and applications, along with visual examples of walks generated by quadratic and cubic functions.

Contribution

It provides a comprehensive framework and visual overview for two-dimensional functional walks, emphasizing notation, definitions, and applications.

Findings

Visual representations of walks generated by f(n)=n^2 and f(n)=n^3

Establishment of notation and definitions for functional walks

Application examples demonstrating the utility of the framework

Abstract

This paper gives a general introduction to two-dimensional functional walks with particular attention to notation and definition. We also give applications of functional walks and a visual overview of some walks generated by $f(n)=n^2$ and $f(n)=n^3$.