[seqfan] The gasket, the set, and the arrowhead.

[Peter Munn]

Hello seqfans,

Following our work in April on Bill Gosper's A019989-A019991, I've got
into the relationship between Sierpinski's gasket and arrowhead, and a
particular sequence (A307744) that came out of my investigations.

This week I spotted an underlying property for the appearance of the
Cantor set in this relationship, and it would be nice to have reference(s)
to cite.

A307744 came from looking at a Sierpinski arrowhead curve as infinite in
extent but composed of unit edges (so without fractal detail), but my new
insight uses the standard view of the curve as the limit of a sequence of
successively more detailed functions [0,1] -> R^2, with its image being
the Sierpinski gasket. My insight: I'm thinking the inverse function maps
each boundary of a triangular region of the gasket's complement to a
scaled (and translated) image of the Cantor ternary set.

In seeking a reference for this, I'm hitting a problem: the gasket, the
set, and the arrowhead appear together in half of all wide-ranging web
pages about fractals, so I get hundreds of search results without finding
what I seek. Is there any better-skilled human search assistance here for
me?

Best Regards,
 Peter