Simple Derivation of the Lifetime and the Distribution of Faces for a Binary Subdivision Model

TL;DR

This paper derives fundamental properties of a binary subdivision model, including the average lifetime of faces and their distribution, linking various applications in physics, computer science, and urban planning.

Contribution

It provides a unified derivation of lifetime and face distribution properties in a binary subdivision model, connecting different research areas.

Findings

Average face lifetime depends on birth-time

Distribution of rectangle faces is balanced

Fundamental properties derived mathematically

Abstract

The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.