Tag Archives: Aperiodic 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

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The Long and the Short

A year-out student Tom Kirby emailed an office of 200 people asking what the convention was for beyond and behind dotted line styles.  No one knew. On-line searches didn’t prove very helpful so in one of those mad delightful collective … Continue reading

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Aesthetics of Aperiodic Tilings

Wang tilings seem to me to be visually more interesting than their plain or decorated aperiodic tiling generators. The various versions of the same Penrose P2 tiling below all look very uniform, with their randomness hardly registering, whilst the randomness … Continue reading

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Find Your Own Space

A randomly distributed sets of points can be considered as the lowest state of architectural order; the placing of the simplest object, a point, with the least degree of structure, being randomly placed. Well distributed point sets are important in … Continue reading

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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

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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

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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

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