Re: Sierpinski polygons

In article <426aa1cd@xxxxxxxxxxxxx>, J.L.M. 863219 <nospam@xxxxxxxxxx>
writes
>Can anyone tell me if these variants on the Sierpinski triangle have
>received much attention?
>
>http://web.onetel.com/~amygdala/articles/scimaths/sierpinski.html
>
>
The bottom one may be in my files - 10 or 15 years ago I looked at the
class of IFS attractors composed of rings of identical, touching,
elements - but I can't be sure off hand that I picked up that one. [ One
can plot the rotations and contractions which produce such attractors;
the plot contains line segments where you can continuously adjust one to
keep in step with changes to the other, and points, such as the
flowsnake (Peano-Gosper curve) with the central element removed. At the
time I only identified pairs of values empirically, with the exception
of a few cases with rotations of 0 or pi/n, and quite possibly missed
some isolated point or line segments.

You don't give a construction for members of the set, so I can't comment
on the set as a whole.
--
Stewart Robert Hinsley
.

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