Meta-intransitive Systems of Independent Random Variables and Fractals

TL;DR

This paper introduces a method to construct complex meta-intransitive systems of independent random variables, generalizing intransitive dice, and explores their fractal properties and similarity dimensions.

Contribution

It presents a novel construction of meta-intransitive systems of any finite order and extends the framework to infinite-order fractal systems with dimension analysis.

Findings

Constructed meta-intransitive systems of any finite order.

Extended the construction to infinite-order fractal systems.

Evaluated the similarity dimension of these fractals.

Abstract

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is preserved, provided this equality hold for the basic variables. This scheme is also extended to infinite-order systems, which are shown to be fractals, and for which the similarity dimension can be evaluated. The problem of the upper bound for this dimension is posed.