Triangular lattices can be very tiny, such as in crystals (metal, diamond, etc) or very large, such as bridge construction. In the very tiny, a Hofstadter butterfly can show up in the data as it does here Can you see it? Left is the plot, right is the Hofstadter butterfly on a triangular lattice.

Triangular lattices can be very tiny, such as in crystals (metal, diamond, etc) or very large, such as bridge construction.
 
In the very tiny, a Hofstadter butterfly can show up in the data as it does here
 
Can you see it? Left is the plot, right is the Hofstadter butterfly on a triangular lattice.
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