Annihilative fractals of coffee on milk formed by Rayleigh-Taylor instability

TL;DR

This paper reports the discovery of a new fractal pattern formed by coffee on milk due to Rayleigh-Taylor instability, revealing similarities to the Sierpinski carpet and expanding understanding of fluid interface fractals.

Contribution

It introduces a novel fractal pattern formed by coffee on milk, linked to Rayleigh-Taylor instability, and suggests a fractal formation rule akin to the Sierpinski carpet.

Findings

Fractal dimension of 1.88 ± 0.06 for coffee patterns

Pattern area decreases exponentially with pattern complexity

Pattern formation follows a rule similar to the Sierpinski carpet

Abstract

We have discovered a new fractal pattern, coffee exhibits on a horizontal surface, with a fractal dimension $1.88 \pm 0.06$, when a heavy coffee droplet interacts with the surface of lighter milk. Parts of coffee pattern on the surface disappear due to Rayleigh-Taylor instability, and the annihilative behavior produces the fractal pattern. Coffee fractals and the Sierpinski carpet have common features, such as the fractal dimension, annihilative behavior, and an exponential decrease of the pattern area. It is suggested the formation of fractal follows a rule similar to that of the Sierpinski carpet.