Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
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Generate a periodic pattern
ResourceFunction["PeriodicPatternGenerator"][{n,{x,y},disp}] creates a periodic square array with a side length of x×y based on repeated x×y rectangles filled with the digits of integer n in base 2 with displacement disp on subsequent rows. | |
ResourceFunction["PeriodicPatternGenerator"][{n,{x,y},disp,b}] uses base b. |
Create a periodic pattern based on the binary expansion of 3::
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Show a binary periodic pattern:
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Show the order 2 binary periodic patterns (horizontal stripes, vertical stripes, checkerboard):
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Show all eight order 3 binary periodic patterns:
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Show all twenty order 4 periodic patterns (with Tooltips):
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These periodic patterns are equivalent by displacement:
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There are 8 order-3 ternary periodic patterns:
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There are 65 order-4 ternary periodic patterns:
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Boring patterns usually have a simpler representation:
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Using PeriodicPatternGenerator, CanonicalListRotation and a brute force algorithm, we can find all displacement-distinct binary patterns up to order 9, given here as a convenience:
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Show all 180 order 5 ternary patterns:
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Show samples of the 129064 order 16 binary patterns:
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