Domino Magnification

TL;DR

This paper analyzes the conditions for a chain reaction of dominoes to continue toppling, focusing on frictionless dominoes and deriving the maximum growth rate for the domino sequence to sustain the effect.

Contribution

It provides a scale-invariant model that determines the maximum growth rate of dominoes for a continuous topple effect based on their separation.

Findings

Derived the maximum growth rate for domino sequences to keep tumbling.

Established a scale-invariant model for domino toppling.

Identified the critical conditions for domino effect sustainability.

Abstract

The conditions are investigated under which a row of increasing dominoes is able to keep tumbling over. The analysis is restricted to the simplest case of frictionless dominoes that only can topple not slide. The model is scale invariant, i.e. dominoes and distance grow in size at a fixed rate, while keeping the aspect ratios of the dominoes constant. The maximal growth rate for which a domino effect exist is determined as a function of the mutual separation.