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As a PhD student in mathematics, I like my coffee - quite a lot. But I'm also poor (because, duh, I'm a PhD student), so my funds available for coffee are pretty limited. In order to still be able to have a decent cup of coffee, I decided to invest in a nice hand grinder and an Aeropress - figuring it would pay for itself.

So, here I am, hand grinding coffee beans, a local barista recommended, brewing what I consider to be surprisingly decent coffee and still - something is wrong.

My coffee - for some reason - has a dragon curve floating on its surface!

Unfortunately - being in my office - I am not able to take a picture of it. But it comes really close to an actual dragon curve, posted below for reference.

Dragon Curve

A dragon infested office clearly isn't suitable to work on ones thesis and hence I sit here, wondering about dragon curves and what might cause one to show up in my coffee cup instead...

Technical details: I'm using a fine - but thin - paper filter in my Aeropress and some blent of mostly Arabica coffee for my beans of a medium grind size. It seems most likely to me that the dragon curve I observe is made of lipids - especially since Arabica (according to a quick internet search) seems to contain a decent amount (~15%). That, however, doesn't explain its fractal appearance. I've seen lipids floating on coffee many times before, but as far as I can remember, they just formed boring puddles or were entirely absent (maybe due to using a thicker filter).

I welcome any attempt, preferably backed by published research, to explain this distracting phenomenon as well as pictures of similar curves formed by lipids on liquid surfaces (preferably coffee).

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    Fun and indeed distracting; coffee and science! (yey) Bummer no pictures. Was it static or changing? Growing like a crystal or non-crystalline? Do lipids in other situations grow into fractal-like crystals? Was this freshly brewed and hot, or old and cooled? I have seen ephemeral sweeping curves on top of hot coffee and tea, which I have assumed is something like water vapor somehow clinging to the surface. I have also seen over-brewed tea or coffee, after resting and cooling, to form a thin "scum" on top. Similar, or more phenomena to explore?
    – hoc_age
    Commented Dec 9, 2016 at 13:00
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    @hoc_age It was 'mostly' stable, but parts of it were rotating slowly. It was hot, freshly brewed, but the curve was still there when my coffee was cold (after posting this question). I think it's different from the 'scum' you observed, but I'm not sure.
    – Stefan Mesken
    Commented Dec 9, 2016 at 15:07

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It's probably not a dragon curve, but the fractal projection of the Brownian motion of coffee lipids on the surface of your tasty beverage.

Brownian motion is best explained by statistical physics. Small atoms or molecules collide each other continuously in very high speeds in the liquids even if they seem serene. However, as the total effect (average) of these collisions are quite stable, we see a still surface.

The small particles, which are very light in mass, can be affected by these collisions. So, they may move with respect to these collisions. So, you can observe these collisions as Brownian motions if you put some very light powder or lipid on top of the surface of a liquid. Very probably, this is what you have experienced.

Here you can find a very comprehensive list of fractal sketches, including the ones related to Brownian motion. Do any of them look similar?

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