I wrote a small program in C++ to arrange wall tiles so that it minimised patterns. I did not want a 'random' pattern as that would have allowed 2 red tiles next to each other. I did this by defining a set of patterns and weighting each set then iterating many times over a grid of tiles moving them, re-scoring the result and keeping the best. I imagine there is a more mathematical way to achieve this but I don't know what to search for.
Is there a field of mathematics concerned with no patterns?
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2What sort of patterns do you want to minimize? – 2012-11-01
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0If you consider two of the same color being neighbors a "pattern," that's a broader meaning of pattern than tends to be used by mathematicians. "Pattern" is usually used to describe a global property - "all red squares are next to a blue square" is a pattern. Even "50% of red squares are next ot a blue square" is a pattern. "One red square is next another red square" is not a pattern. – 2012-11-01
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2In fact, banning adjacent tiles having the same colour can lead to very strong patterns. If you have two colours in a square grid, and you don't allow two (orthogonally) adjacent squares to be the same colour, then you've forced yourself into a regular chessboard pattern. – 2012-11-01
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0I had 4 colours and as I said weighted rather than banned patterns. The kitchen is now tiled and it achieved exactly the effect I wanted (no patterns) but I ran the program overnight to achieve a kitchen's worth of arrangement. – 2012-11-01
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0@Jonah Anything that the human identifies as a pattern. So same coloured tiles in a row, more than 3 diagonally, crosses made of only 2 colours. Anything that doesn't look 'random' in the 'no pattern' sense of the word. – 2012-11-01
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0@ThomasAndrews I suspect I am using the wrong term when I say 'pattern' because I could not find any information on methods of reducing patterns. – 2012-11-01
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0Yeah, there isn't much known about what the human mind "sees" as a pattern. The human mind is designed to make order in a disordered world, and there is no precise mathematical definition of what a human will see as a pattern - one person might look at a figure and see a pattern while another will not. As such, this is not really a math question. – 2012-11-01
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0If we forget the application and just look at the requirements of taking a pile of coloured tiles and arranging them in an order that minimises the occurrence of pre-defined arrangements - is there a mathematical field in which this could be expressed? – 2012-11-01