einstein hats
einstein hats create aperiodic tiling — a pattern that never ever repeats! From the German “one stone” (and the brilliant physicist), the math shape can create an infinite plane and may help us puzzle together pieces of the universe. The shape was discovered and mathematically proofed in 2023 by David Smith, a non-mathematician and serves as a model for quasicrystals.
aperiodic tiling
aperiodic tiling may also provide clues for space-time fabric in cosmology, as referenced in this other interesting WHITE PAPER from 2024
mathematically proved
“An aperiodic monotile, sometimes called an ‘einstein’, is a shape that tiles the plane, but never periodically. In this paper we present the first true aperiodic monotile, a shape that forces aperiodicity through geometry alone, with no additional constraints applied via matching conditions. We prove that this shape, a polykite that we call "the hat", must assemble into tilings based on a substitution system. The drawing above shows a patch of hats produced using a few rounds of substitution.”
