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anyway in lieu of taking a nap I have been meaning to talk about this little free casual game I've been playing as my "bored and have 2 minutes to kill" game, called Tessel (available on web and as an iOS/Android app). To my indignation it is in fact more than a mindless time-waster and I ended up learning about MATH!!! >:(

It is a simple game where there are multicoloured polygons that fit together, but you can only attach sides with the same colour. (There's also a custom mode where you can change the rules, number of colours, etc.) You get points for how many tiles a resulting colour block covers, and you only get a certain number of tiles (only a few are available to choose from per turn, but you can shuffle them as many times as you want). The game records your high score for each shape.

🧵

#gameing #math

Neville Park

@nev@status.nevillepark.ca replied · last week

You may recognize the squares as Wang tiles like in that one Greg Egan story where they're used to make a Turing machine that simula—anyway, not the point, the point is that putting a bunch of shapes together is an entire field of geometry, called tessellation or tiling. Eggheads are really out there thinking up weird new shapes to make tiles of. In the game you can actually play games with some of these tilings, like Ammann–Beenker and Penrose tiles.

(I like the Penrose tiles because there are pretty flower- and star-like sub-patterns they sometimes make, but starting from just one piece and matching as you go, you can't really tell what part of the pattern you are in, unlike the majestic and ever-symmetric beauty of the hexagon.)

Alex, the Hearth Fire

@WizardOfDocs@wandering.shop replied · last week

@nev I'm gonna have to try this game

Neville Park

@nev@status.nevillepark.ca replied · last week

Anyway, I was mystified by how the game designer settled upon the number of tiles per game type (why 70 instead of 30, or 100?), although I figured it had something to do with the various combinations possible with the number of sides and the number of colours, as the more complex shapes had more tiles.

One day in the shower I started wondering, given a simple polygon with n sides and a set of x colours with anywhere from 1 to x colours per tile, how many different combinations there would be. To my horror I realized this was also math.

(I asked the designer, who explained it's based on total possible unique tiles, except for when that would be too low.)

Neville Park

@nev@status.nevillepark.ca replied · last week

There is a vast world of tessellations and special notations to describe them and whatnot.

Anyway, Tessel, fun game, check it out. Any tips for how a "technical" player might use math to optimize play are welcome.

P. S. My current mathematical rabbit hole is about scoring. The game records your high score, but 1) there is a different high score for each shape type, and 2) only with the default 4 colours and 3) only with the default number of tiles (you can now choose to generate more tiles at the end of the game, but that means your score doesn't count for high scores).

I feel it ought to be possible to make a sort of combined score that factors in number of colours, number of sides, and total number of tiles. It should be possible to calculate, like, how many points per colour per side or whatever, right? Some kind of "efficiency score". 🤔

Neville Park

@nev@status.nevillepark.ca replied · last week

P. P. S. I am absolutely the kind of person who is completely uninterested in math or programming until it applies to a problem I want to solve, like "how get more points in game"

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