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Up: Strip Patterns
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Let's try and understand patterns which repeat along an infinite strip. We
want there to be a group of rigid motions taking the strip to itself as well
as the pattern to itself. The group should include all multiples backwards
and forwards of a particular translation. By choosing which way to orient
and scale our coordinates, we can normalize the strip to be
and the smallest translation
to the right one unit; i.e.
It turns out there are only 7 essentially different symmetry groups
which can arise this way ! The program Kali lets us pick one of
these, draw a pattern and see what the symmetries do.
Let's try and understand how one can come up with a conclusion
like this result that only 7 possibilities exist. As you think
about some of the questions below, experiment with Kali to try
and get some insight.