Discovered Tilings
Infinite Number of Prototiles
An one-dimensional substitution rule that uses an infinite number of prototiles.
The inflation factor is $2.5$.
The substitution rules are given by:
$T_{0}\rightarrow T_{0},T_{1}$
$T_{1}\rightarrow T_{0},T_{0},T_{2}$
$T_{2}\rightarrow T_{0},T_{1},T_{3}$
$T_{k}\rightarrow T_{0},T_{k-1},T_{k+1}$ …
One Dimensional Self Similar Substitution