On the Sierpinski triangle and its generalizations

TL;DR

This paper explores fractal structures emerging from arithmetic operations in various bases, extending the classic Sierpinski triangle to more general forms.

Contribution

It introduces a new framework for understanding fractal patterns generated by arithmetic in different bases, generalizing the Sierpinski triangle.

Findings

Fractal structures are revealed through decimal arithmetic in various bases.

Generalizations of the Sierpinski triangle are characterized mathematically.

New patterns extend the classical fractal to broader contexts.

Abstract

By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle