In higher dimensions, tiling can devolve into nonrepeating chaos, overturning the periodic tiling conjecture and revealing how disorder emerges from mathematical structure.
The periodic tiling conjecture suggested that any shape able to tile space must do so in a repeating manner; our study disproves this notion by introducing a strictly aperiodic tile.
We translated the geometric tiling problem into an algebraic one, using a system of equations that encapsulates the constraints required for proper tiling.
This ground-breaking discovery indicates that even structured mathematical forms can lead to disorder, showcasing the complexity and unexpected outcomes inherent in higher-dimensional spaces.
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