Illustration of how to convert from traditional axial (or cubical) hex coordinates to and from two one-dimensional
enumerations based on space-filling fractal curves.
The spiral honeycomb mosaic enumeration recursively labels nested “super hexes” in base 7, starting from 0 at the origin.
The flowsnake enumeration also call “Gosper7” here, recursively labels the same super hexes but in a continuous
sequence with no jumps.
This uses a negative base 7 with an unbalanced signed representation using the digits = (-2), - (-1), 0, 1, 2, 3, and 4.
These enumerations could be useful for compact visualization of one-dimensional sequence data
as well indexing hexagonal data storage with good locality properties similar to the Hilbert curve.
This example shows a simple visualization of the structural protein sequence for covid-19,
with individual amino acids mapped to a standard color palette.
The flowsnake embedding induces a characteristic boundary shape based on its length,
with the snake’s compact “folding” reminiscent of (but completely unrelated to) protein folding,
which perhaps provides a useful visual fingerprint for the sequence.