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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
Tagged Aperiodic Tiling, Architecture, Design Methods, Geometry, Logic, Tiling, Turing Machines
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
Tagged Aperiodic Tiling, Architecture, Geometry, Tiling, Turing Machines
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 Aperiodic Tiling, Geometry, Tiling
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 Aperiodic Tiling, Geometry, Tiling
5 Comments
Periodic and NonPeriodic Tiling
The concepts of periodic and nonperiodic 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
Tagged Aperiodic Tiling, Architecture, Geometry, Tiling
3 Comments