# Tag Archives: Tiling

## William Tutte’s Hidden Past

If William Tutte is remembered at all by architects, it is for his contribution to solving the problem of Squaring the Square . (Tutte 1958) A solution using Graph Theory and Kirchhoff’s Laws for electrical flow in wires that was subsequently used in Philip … Continue reading

Posted in Architecture, Design Methods, Geometry, Logic, Tiling | | 3 Comments

## Wang Tiles and Turing Machines

Wang pointed out that it is possible to find sets of Wang tiles that mimic the behaviour of any Turing Machine (Wang 1975). A Turing machine can compute all recursive functions, that is functions whose values can be calculated in … Continue reading

Posted in Aperiodic Tiling, Architecture, Geometry, Tiling, Turing | | 22 Comments

## Wang Tiles and Aperiodic Tiling

Wang originally conjectured that no aperiodic tilings could exist. Wang was interested in the decidability of the Tiling Problem; it is said to be decidable if there exists an algorithm which will yield a solution for any given set of prototiles … Continue reading

Posted in Aperiodic Tiling, Architecture, Geometry, Tiling | Tagged , , | 13 Comments

## Aperiodic Tiling

This closely follows “Tilings and Patterns” (Grünbaum and Shephard, 1987), but uses coloured diagrams rather than their monochrome ones. In some ways this is simply a catalogue of aperiodic tilings, their various forms and some indication of their uses, but my interest … Continue reading

Posted in Aperiodic Tiling, Architecture, Geometry | Tagged , , | 6 Comments

## Periodic and Non-Periodic Tiling

The concepts of periodic and non-periodic tiling are defined so as to clearly distinguish them from aperiodic tiling; the subject of a future post “Aperiodic Tiling”. Informally a tiling (of the 2D Euclidean plane) is a collection of subsets of … Continue reading

Posted in Aperiodic Tiling, Architecture, Geometry, Tiling | | 4 Comments