Rep-Tiles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A 2D shape that can tile itself with smaller, equally sized copies of itself is called a rep-tile and is said to be rep-.

[more]

The order of a rep-tile is the smallest number such that the tile is rep-.

Any polysquare that tiles a square is obviously a rep-tile. These trivial cases are omitted here.

[less]

Contributed by: Karl Scherer (January 2016)
Additional contributions by: George Freeman and Erich Friedman
Open content licensed under CC BY-NC-SA


Snapshots


Details

A shape that tiles itself using different sizes is called an irregular rep-tile (or irreptile). Irreptiles are investigated in a separate Demonstration.

Reference

[1] M. Gardner, "Rep-Tiles," The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, New York: W. W. Norton & Company, Inc., 2001 pp. 46–58.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send