Ending the cycle means recognizing subtle violations early and responding differently. It means understanding that clarity ...

Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

Why do the same, self-repeating patterns appear in trees, rivers, lightning, and even our bodies? Why do the same, self-repeating patterns appear in trees, rivers, lightning, and even our bodies? Is ...

Experiments and modeling work offers new insights into the striking patterns of repeating stones seen in frost-prone landscapes. Nature is full of repeating patterns that are part of the beauty of our ...