Definition
Plain language
A shape that repeats the same pattern inside itself at smaller and smaller scales.
As stated in the literature
A self-similar geometric structure whose sub-parts are scaled copies of the whole; arises naturally in recursive state spaces such as the Tower of Hanoi move graph.
Also called: fractals
Why it matters: Recognizing that a problem's space of possible situations has this repeating structure lets researchers reason about the whole from a small piece of it.
For example, zooming in on one corner of a fern-like shape reveals a smaller copy of the whole fern, and zooming in again reveals a smaller copy still.
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