Kenyon's Construction
As well as showing that there are substitution rules for every Perron Inflation Factor, [Ken96]
gives an explicit construction for expansion factors $x$ with $x^n - p x^n-1+qx + r =0$, where $n,p,q,r$ are integers with $n>2, r$ positive, $p,q$ non-negative.
As well as showing that there are substitution rules with any Perron
inflation factor, in [Ken96]
, R. Kenyon
gives an explicit construction for the Perron numbers that satsify:
$xn - a xn-1 + b x + c$, where $a, b$, and $c$ are natural numbers.
This is an example of that method given in that paper. …
Finite Rotations Self Similar Substitution Kenyons Construction
A polygonal version of Kenyon (1,2,1). The boundary is generated by the morphism $a \to b, b \to c, c \to c a' b' b'$ (where $x'$ is the inverse of $x$).
Finite Rotations Polytopal Windowed Tiling Canonical Substitution Tiling Parallelogram Tiles Kenyons Construction
References
[Ken96]
Kenyon, Richard
The construction of self-similar tilings
Geom. Funct. Anal.
1996,
6, 3,
pp. 471--488,
MR1392326