Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show that each of the new tilings is mutually locally derivable to the original tiling. Thus, at the tiling space level, the new substitution rules are expressing...

We aim at a conceptually clear and technical smooth investigation of Ackermann’s substitution method. Our analysis provides a direct classification of the provable recursive functions of PA , i.e. Peano Arithmetic framed in the ε-calculus.

Revisiting Penal Substitution Kevin D. Kennedy Assistant Professor of Theology Southwestern Baptist Theological Seminary 2001 W. Seminary Drive Fort Worth, Texas 76115 Jesus paid it all, all to Him I owe; Sin had left a crimson stain, He washed it white as snow. Evangelicals, in their preaching as well as their worship, have recognized that the cross of Christ is central to the life of the beli...

The substitution closure of a pattern class is the class of all permutations obtained by repeated substitution. The principal pattern classes (those defined by a single restriction) whose substitution closure can be defined by a finite number of restrictions are classified by listing them as a set of explicit families.

We perceive just a tiny proportion of the phenomena that surround us everyday. Sensory Threads is a technologically mediated collective sensing expedition which allows people to explore imperceptible phenomena in the world around them. We present a description of the technical system and reflect on our design decisions. Key questions we are concerned with centre around how to represent impercep...

Square Root Palindromes ................................... 1 Sigma Quest .......................................................... 6 Decimal Fractions ................................................ 9 Designing Weavable Color Patterns ............... 12 Polygraphic Substitution .................................. 17 Programming Tips ............................................. 20 What’s Comi...