On a generalized Sierpinski fractal in RP^n

TL;DR

This paper introduces a generalized Sierpinski fractal in real projective space, analyzing its measure, asymptotic behavior, and Hausdorff dimension for dimensions 1, 2, and 3.

Contribution

It defines a new class of fractals in projective space associated with vector bases and studies their geometric and measure-theoretic properties.

Findings

Fractal measure and asymptotic properties characterized.

Numerical evaluation of Hausdorff dimension for n=1,2,3.

Insights into the geometric structure of the fractals.

Abstract

We associate a fractal in $\RPn$ to each vector basis of $\bR^{n+1}$ and we study its measure and asymptotic properties. Then we discuss and study numerically in detail the cases $n=1,2,3$, evaluating in particular their Hausdorff dimension.