The names flowsnake, Gosper island, Gosper curve and Peano-Gosper curve have been applied to the directly self-similar cyclic heptahextal. I extend the name to include the corresponding inversely self-similar tile, distinguishing them as the cis-flowsnake and the trans-flowsnake.

The elements of the above figures can be considered as centred on 7 points
of a hexagonal grid (e.g. at the Eisenstein integers `e _{00}`,

I conjecture that these two series of tiles have a countably infinite number of members, as there is no obvious reason why the construction should stop working at any point.

Each element of an n^{th} order flowsnake is contracted by `√(3n ^{2}+3n+1)` and rotated by

These obviously tile the plane with one copy in the unit cell. With the
above orientations and placement of elements on a unit grid the tiling vectors
are e_{n0} + e_{nn} + e_{11} and e_{n0} +
e_{10} - e_{0n}.

**Source:** All are independently discovered, except that the angle by
which the elements of the *cis 1st order flowsnake* are rotated was
derived from an L-system construction given in Scientific American.

© 2000, 2017, 2018 Stewart R. Hinsley