It is a square number (33 squared), a nonagonal number, a 32-gonal number, a 364-gonal number, and a centered octagonal number. 1089 is the first reverse-divisible number.
This was similar to the piano roll developed at the end of the 19th century and may have been inspired by the patterns that were traditionally drawn on squared paper.
Also, the amplitude of infragravity waves increases dramatically with the wave period (typically like the period squared), which results in higher run-up.