Mathematicians make even better never-repeating tile discovery

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A patch of spectre tiles. Some tiles are considered odd (shaded) and even (not shaded) based on their orientation


A patch of spectre tiles. Some tiles are considered odd (shaded) and even (not shaded) based on their orientation

https://cs.uwaterloo.ca/~csk/spectre/

Mathematicians solved a decades-long mystery earlier this year when they discovered a shape that can cover a surface completely without ever creating a repeating pattern. But the breakthrough had come with a caveat – both the shape and its mirror image were required. Now the same team has discovered that a tweaked version of the original shape can complete the task in just one orientation.

Simple shapes such as squares and equilateral triangles …



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