A spirolateral is a continuous path drawn by repeating a sequence of
line segments of lengths
with a given angle
of turn between each line segment and the next one. (Alternatively
the path can be considered as a repeated sequence of 'bound' vectors:
, each vector starting at the endpoint
of the previous vector.)
In the first diagram the lengths of the line segments are equal and the
angles of turn vary periodically in sequences of length 3. In the second
diagram the lengths of the line segments vary periodically in sequences of
length 5 and the angles of turn are equal. In the third diagram both the
lengths and the angles vary.
Investigate these patterns, give sequences of instructions which
would produce similar paths and explain why in each case the
spirolateral paths are closed producing a cyclic pattern when the sequence
is repeated infinitely often.
Why does the spirolateral in this diagram continue
indefinitely, shooting off to infinity if the sequence is
repeated infinitely often?
