Solution by sharing

Pardon our preoccupation with the uncanny moment tiling has been having, but here we go again with another tile mockup. First there were Penrose tiles, which worked as a set of two shapes, but hadn’t been reduced to one. The Hat, or Shirt, tile was the first single shape discovered to tile without ever repeating the tiling pattern. The only possible catch was, some tiles were flipped, which gnawed at the purist in some observers. It tended to light a fire under actual tile manufacturers as well.

Just when your shower wall was finished

In an unprecedented turnaround, the same folks, despite evidence out there for anyone to sieze, blew through that barrier too. Playing, sharing and communicating seemed to be among the driving forces. The new shape, called the Spectre, can be made chiral, or left or right-handed, which defies repetition without flipping. So all of the shapes in each of today’s games are identical, just set at various angles. They piggyback on the basic Spectre shape, which has straight equilateral sides, but can itself flip. As is the convention with all tiles, there are no overlaps or gaps.

Shape shifters

Arbitrary tweaks to Spectre’s basic sides, which won’t work with the Hat, are the key to obviating flipping. With imagination, these tweaks can end up making the shape look like Escherian creatures or objects. We fiddled with our first try to make a Yorkshire Terrier as a film noir-style detective wearing a fedora. See if you can see this tip of the hat to the Hat, Trace Yorks, in the first game below. The green one left of center with the L has about the right orientation we envisage.

In both our and Blu Yonder’s efforts, we sussed out words beyond the words, faux-cabulary, with definitions to match. They got no points, but served to get our creative juices flowing, and maybe yours too. Enjoy them as is, with a cold beverage, feeling free to gong the duds through the backstage wall. When you play the game yourself, defend your own favorite phonies on the hill of your choice for extra kicks. Please note the usual display disclaimers apply: Because it’s a mockup rendering, some colors don’t stand out well, etc..

Spectre noir-terrier tile user screenshot (chiral aperiodic monotile)
As always with puzzle-piece-type patterns, letters are considered adjacent if their surrounding shape edges touch. If only the corners meet, it’s not a word-forming connection. For spilled objects like hearts, they’re touching even if only the pointy corners of hearts meet.

Made for TV

Jiglit: (Computer graphics) A visual object given the appearance of springiness.
Gunole: A branch of pneumatic tubing, as used for physical message delivery.
Telofise: To adapt, as a story, for television; Used pejoratively, to reduce to a lowest common denominator for mass consumption; To dumb down.
Litrany: A listicle of complaints submitted by multiple online participants in response to an open question.
Folet: The palette of sounds created by a Foley artist, often for a particular film.
Unofise: To appropriate or repurpose the boards, pieces, cards, etc., of one game as props in creating a new game. Not that tiling was an established game, but that’s kind of what we’re doing here.

Spectre noir-terrier tile Blu Yonder screenshot (chiral aperiodic monotile)
Built-in player Blu Yonder topped us by over 100 points using the same letters and designated tiles. No special scoring rules applied here.

Oscar, Oscar, Oscar

Igaret: A slim statuette of a human figure.
Yarent: Idealistic; Wishful; Unattainable; Untenable: Don’t try to be something yarent.
Sentile: Able to be sensed.
Garset: A bodice.
Yoself: (Interjection said to one who has just reprimanded or criticized the speaker) Likewise.
Felite: Appropriate; Advantageous; Felicitous.

Spectre jigsaw-like tile user screenshot (chiral aperiodic monotile)
We actually goofed the setup for this one. A typo caused the tiles with the D and O on the left to be considered connecting, instead of the D and S tiles. So ADO shouldn’t count, and ADS should, etc., for both us and Blu Yonder.

Time dilation

Pring: A ring (for pulling) connected to a bathtub plug, bus stop signal, etc.
Spand: Rubbery sand used in hourglasses measuring time in time travel settings.
Oing: The sound of a truncated jiglit.
Scrab: A leftover morsel of food.

Spectre jigsaw-like tile Blu Yonder screenshot (chiral aperiodic monotile)
This time we outdid Blu Yonder even though we bungled a little plan. The plan would’ve required an E, which didn’t come up anyway.

Have a nice trip

Cusap: A condiment similar to maple syrup.
Ragosa: Leafy vegetables used in cooking.
Goap: The gooey residual part of soap that has been continually moistened.
Parsnag: A root vegetable grown to trip rabbits, voles, etc., encroaching on crops: After the Great Parsnag Faceplant of ’22, Peter never again ventured into Farmer McCormick’s carrot patch. Parsnag FTW.

Spectre gadgets

For a little background on the Spectre tile (technically a chiral aperiodic monotile), here a couple of links. One YouTube video from Numberphile veteran and portmanteau fan Ayliean MacDonald, and a Gathering 4 (Martin) Gardner group video discussion featuring several key players in the story. And here’s the accessible scientific paper documenting the discovery. Special thanks to the authors for making their interactive web app available for populating a plane. And to Yoshiaki Araki and colleague apu_yokai for the Desmos tool for freely deforming the boundary using control points.


No Comments

Add your comment