Abstract
We extend the diffraction calculations made by Spindeler [(2017), PhD thesis, Bielefeld University] and Gohlke [(2017), Master's thesis, Bielefeld University] to a family of two-dimensional constant-shape random substitutions and a nonconstant-shaped example. Specifically, we consider a family of binary constant-shape random block substitutions of size
k
×
k
defined by the rule \vartheta:b\ \ \mapsto\ \ a^{k\times k}, a\ \mapsto {\vartheta^{(i)}(a) with probability p_{1}\mid 1\leq i\leq N-1}, where k\in{\bb N},
p
i
> 0 for all 0 ≤
i
≤
N
− 1 and \sum_{i = 0}^{N-1}p_{i} = 1 with
a
k
×
k
and each ϑ
i
(
a
) is a square block of size
k
×
k
. We illustrate that their corresponding systems have a mixed spectral type consisting of a pure-point part and a continuous part that is only fully absolutely continuous. We also explore extending the computation to random Fibonacci direct product variation, presenting a heuristic diffraction framework for the class of nonconstant-shape but geometrically compatible inflation rules.