To refresh, the question was what the pattern/generalization of this design is:
___ ___ ___ ___ ___ ___ ______
\ / \ / \ / \ / \ / \ /
\ \ \ / / /
___/ \ / \ / \ / \ / \ / \ ___
\ / \ / \ / \ / \ / \ /
\ \ \ / / /
___ / \ / \ / \ / \ / \ / \___
\ / \ / \ / \ / \ / \ /
/ / / \ \ \
___/ \ / \ / \ / \ / \ / \ ___
\ / \ / \ / \ / \ / \ /
/ / / \ \ \
___ / \ / \ / \ / \ / \ / \___
\ / \ / \ / \ / \ / \ /
/ / / \ \ \
___/ \___/ \___/ \___/ \___/ \___/ \______And the answer is that if you chop the pattern up into four quadrants, and the crossings all go the same way within each quadrant, like so:
___ ___ ___ ___| ___ ___ ______
\ / \ / \ / \ / \ / \ /
\ \ \ |/ / /
___/ \ / \ / \ / \ / \ / \ ___
\ / \ / \ /| \ / \ / \ /
\ \ \ | / / /
___ / \ / \ / \| / \ / \ / \___
---\-/---\-/---\-/---\-/---\-/---\-/------
/ / / |\ \ \
___/ \ / \ / \ / \ / \ / \ ___
\ / \ / \ /| \ / \ / \ /
/ / / | \ \ \
___ / \ / \ / \| / \ / \ / \___
\ / \ / \ / \ / \ / \ /
/ / / |\ \ \
___/ \___/ \___/ \___/ \___/ \___/ \______This can be scaled up or down to any number of bands, for example the classic design is four bands
___ ___ ___ ___ ______
\ / \ / \ / \ /
\ \ / /
___/ \ / \ / \ / \ ___
\ / \ / \ / \ /
/ / \ \
___ / \ / \ / \ / \___
\ / \ / \ / \ /
/ / \ \
___/ \___/ \___/ \___/ \______And it can be chopped into quadrants as well
___ ___ ___| ___ ______
\ / \ / \ / \ /
\ \ |/ /
___/ \ / \ / \ / \ ___
------\-/---\-/+--\-/---\-/---
/ / | \ \
___ / \ / \| / \ / \___
\ / \ / \ / \ /
/ / |\ \
___/ \___/ \___/ \___/ \______I also gave the three banded version in a previous post. The five-banded design works as well, but I don't like that as much because it doesn't have a strong canonical position which the bands want to go into like they do with four or six.
