Kites, Triangles, and Hexagons: Inside the Hat
over 2 years ago
– Wed, Oct 18, 2023 at 11:01:24 AM
When we play with InFUNity Tiles, shapes within and between the shapes emerge, as do design possibilities.
The first shape to be aware of is the kite. A kite is four-sided shape like an arrowhead, with one stubby end and one long pointy end, as it were, like this:
Three kites can together form an equilateral triangle:
And six kites can make a hexagon:
As it happens, the Hat and the Turtle aperiodic monotiles are both constructed of kites. Here's how they fit together:
What this means is that when you assemble a field of aperiodic kites and/or turtles, they inherently create overlaying periodic fields of hexagons and triangles at several scales.
Consider the "infinite bullseye" of triangles expanding at increasing scales when drawn over an assembly of hats or turtles:
Similarly, here's the "infinite bullseye" of hexagons that emerge from the kites within a field of hat or turtle tiles:
Extend the smallest hexagons or triangles outward, and you get an "infinite grid." And you can do the same with any of the scales of hexes and triangles in the "infinite bullseye," actually.
As game designers, that hex grid really excited us, and helped convinced us to produce InFUNity Tiles in mass quantities.
Think of a classic game like Settlers of Catan, which uses hexes for resource generation. Imagine in our diagrams above that grey represents mountains, green is forest, and yellow is fields. Each hex formed by a random construction of hat tiles would let a game designate mixed resources from a hex either in a 2:1 ratio, or a 3:0 ratio (if connecting hats are the same color). We can imagine a resource management game where you collect 2 lumber and 1 ore for occupying a green/grey hex, for example.
Our kiddos have had tons of fun drawing kites on our hat prototypes. We suspect there are countless other games and game applications waiting to be developed using this shape, once InFUNity Tiles are easily available to everyone around the world. What new idea will YOU come up with? Tell us in the comments!
-Michelle Nephew & John Nephew, Atlas Games Owners