2-Variable Boolean Operation -- its use in Pattern Formation

TL;DR

This paper explores the use of 2-Variable Boolean Operations on n-bit strings to generate and analyze various patterns, including fractals, with potential applications in modeling natural phenomena.

Contribution

It introduces a mathematical framework for 2-VBO to produce and classify complex patterns, linking Boolean operations to natural and mathematical structures.

Findings

Patterns include fixed, periodic, chaotic, and complex forms.

Some patterns correspond to natural fractals.

Mathematical analysis aids understanding pattern formation.

Abstract

In this paper the theory of 2-Variable Boolean Operation (2-VBO) has been discussed on a pair of n-bit strings. 2-VBO serves to bring out the relation between numbers which when plot on a 2-D surface form interesting patterns; patterns that may be fixed, periodic, chaotic or complex. Some of these patterns represent natural fractals. This paper also provides mathematical analysis corresponding to each of the obtained patterns, which would aid to understanding their formation. 2-VBO is an attempt towards the production and classification of patterns which represent various mathematical models and naturally occurring phenomena.