Definition
Plain language
A triangle made of smaller triangles made of smaller triangles, repeating forever.
As stated in the literature
A classic self-similar fractal; the state graph of the Tower of Hanoi is isomorphic to it, with corners corresponding to single-peg configurations and sub-triangles partitioned by the largest disk's position.
Also called: Sierpinski triangle
Why it matters: Its exact correspondence to the layout of Tower of Hanoi positions means the puzzle's whole space of situations has a precise, predictable geometry researchers can compare a model's internal representation against.
For example, if you draw a triangle, cut a smaller upside-down triangle out of its middle, and repeat that on each of the three pieces left over forever, you get this shape.
Heard on the show
“It's a Sierpiński triangle — the fractal.”Episode 237 — The Model Built a Perfect Map of the Puzzle, Then Lost It