spectre

the spectre is a soldering kit and a colorful puzzle.

discovered in 2023 the spectre shape is an aperiodic monotile that can lay a floor seamlessly. arrangements can never repeat.

here turned into an electronic puzzle where colors can never repeat. you can combine the tiles in many ways, and there are jumpers that both lock the tiles mechanically and also dial in a color for the neighbouring tile. so the color pattern will always depend on the puzzle arrangement but also on the jumpers being set. not all jumpers are required.

one tile is the black tile and this one has no LED, but instead injects power from a 9V block battery (not included) into the system. you can also power it from the back or from a PSU (not included) with a useful voltage range from 5V to 12V.

kit contents

basic kit:

7 white spectre boards
1 black spectre be power board
9V battery connector
a bag of 112+ 01x02 pins
a bag of 100+ jumpers
a QR code to the project homepage

expansion kit (in case you have the basic kit already and want to grow):

8 white spectre boards
a bag of 112+ 01x02 pins
a bag of 100+ jumpers
a QR code to the project homepage

spectre shape origin

neither the name nor the shape is our invention. the shape was found only in 2023 by math researchers as the first single shape known that can seamlessly cover a floor without any gaps, and can never repeat, i.e. is aperiodic.

it’s like the much wider (or longer) known penrose tiling that uses two shapes to create an aperiodic tiling, but with a single tile and 50 years younger.

a very similar shape was found in late 2022 by the recreational mathematician David Smith, his tile was named the “hat”. but a certain percentage of hat tiles had to be flipped front to back to create an aperiodic tiling. then in 2023 he worked with Craig Kaplan, Joseph Samuel Myers and Chaim Goodman-Strauss to find the “spectre”, a single monotile that can tile a floor without gaps or flipping.

their paper can be found here: https://cs.uwaterloo.ca/~csk/spectre/

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