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: $T_{0}\rightarrow T_{0},T_{1}$ $T_{1}\rightarrow T_{0},T_{0},T_{2}$ $T_{2}\rightarrow T_{0},T_{1},T_{3}$ $T_{k}\rightarrow T_{0},T_{k-1},T_{k+1}$ $T_{\infty}\rightarrow T_{0},T_{\infty},T_{\infty}$ The corresponding substitution matrix can be written as: $1 2 1 1 1 1 1 1 1 …$ $1 0 1 0 0 0 0 0 0 …$ $0 1 0 1 0 0 0 0 0 …$
One Dimensional
Self Similar Substitution
