New fractal pattern found in milk and coffee

coffee-fractal.jpg

Next time you stare into your 9am double tall latte, look with new respect. Japanese scientists have discovered a new type of fractal in the patterns coffee makes as mixes with milk.

Placing a heavier fluid onto a lighter fluid always results in an disturbance at their boundary
known as a Rayleigh–Taylor instability.

Michiko Shimokawa and Shonosuke Ohta from Kyushu University in Japan placed coffee (Nescafe’s Gold Blend, if you must know) on top of ordinary milk, which is lighter, and watched how gravity and surface tension compete in a way that leads to Rayleigh-Taylor instability.

As soon as the coffee droplet is placed on the surface, the coffee solution spreads out creating a fractal pattern. But this is a different kind of pattern from the ordinary fractals seen in river branches, and bacterial colonies, which continue to grow and increase in area.

Instead, in coffee, parts of the pattern disappear as they are sucked into the milk by gravity. The result is a shifting pattern, parts of which continually disappear..

Shimokawa and Ohta say this behaviour closely matches that of a Sierpinski carpet which is formed by cutting a square into 9 smaller squares in a 3-by-3 grid. The central square is then removed and the procedure applied to the remaining 8 squares ad infinitum. This creates  a fractal structure with dimension 1.88.

That’s the same dimension that the coffee fractals turn out to have. And there are other similarities too, such as the disappearing patterns.

This, say the Japanese pair, strongly implies that the coffee fractal must form in the same way as a Sierpinski carpet, following similar rules. Intriguing!

So come on chaps: what are these rules and how do they come about in a system dominated by the complexity of Rayleigh-Taylor instabilities?

Ref: arxiv.org/abs/0809.2458: Annihilative fractals of coffee on milk formed by Rayleigh–Taylor instability

3 Responses to “New fractal pattern found in milk and coffee”

  1. [...] New fractal pattern found in milk and coffee [...]

  2. [...] Annihilative fractals found in milk and coffee 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. Annihilative fractals of coffee on milk formed by Rayleigh-Taylor instability http://arxiv.org/abs/0809.2458 New fractal pattern found in milk and coffee [...]

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    regards,
    Fractal John Doe
    -Fractal Math for civilisation advancement.