It is well known that, given an endofunctor H on a category C, the initial (A+H−)-algebras (if existing), i.e., the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys...

generate recursively the infinite Prouhet-Thue-Morse word 0110100110010110 and Fibonacci word 01001010010010100101, respectively [1]. What can be said about the entropy (loosely, the amount of disorder) if we introduce some randomness into such definitions? If [2, 3] ⎨⎩ 0→ 1⁄2 01 with probability 12 10 with probability 12 1→ 0 with independence assumed throughout, then the set of possi...

Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for these new examples, and, in fact, for all substitution tilings showing tiles in infinitely many orientations. Dedicated to my teacher Ludwig Danzer on the occasion of his 80th birthday

Ubiquitous interaction places the user in the centre of dynamic configurations of technology, where work not necessarily is performed through a single personal computer, but supported by a multiplicity of technologies and physical devices. This paper presents an activity-theoretically based framework for analyzing ubiquitous substitution, i.e. a set of mediators that are or can be continuously ...