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 …

An one-dimensional substitution rule that uses an infinite number of prototiles.

The inflation factor is $2.5$.

The substitution rules are given by:

$T_{0}\rightarrow T_{0},T_{1}$

$T_{1}\rightarrow T_{0},T_{0},T_{2}$

$T_{2}\rightarrow T_{0},T_{1},T_{3}$

$T_{k}\rightarrow T_{0},T_{k-1},T_{k+1}$ …