The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities

TL;DR

The paper introduces the $p\lambda n$ fractal decomposition, a mathematical method for exactly partitioning conserved physical quantities into fractal functions, applicable to Hamiltonians and partition functions.

Contribution

It presents a novel fractal decomposition technique that precisely splits functions representing physical quantities into fractal components.

Findings

Enables exact partitioning of physical quantities into fractal functions

Applicable to Hamiltonians and statistical ensemble functions

Provides a new tool for analyzing conserved quantities in physics

Abstract

A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (generally fractal functions), the decomposition being both exact and valid everywhere on the domain of the function.