An one-dimensional substitution rule that uses an infinite number of proto tiles and yields a transcendental inflation multiplier.
The inflation factor is approximately $2.7899$.
The substitution rules are given by:
$T_{0}\rightarrow T_{0},T_{1}$
$T_{1}\rightarrow 3T_{0},T_{2}$
$T_{2}\rightarrow …
One Dimensional Self Similar Substitution