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A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

Like scientific puzzles, Bongard problems can lead you through a frustrating blind search until you find that simple, elegant rule that fits a seemingly random pattern.

For your frustration, joy and entertainment, our puzzle challenges you to find general patterns or rules based on seemingly random, specific examples.

New research has prompted a resurgence of interest in the patterning mechanisms Alan Turing proposed 60 years ago.

A new collection of arresting wallpaper designs seems to defy the crystallographic restriction.

All complex correlated systems, from Arctic melt ponds to the Internet, appear to be governed by the same math as a random matrix.

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