Rep-Tile

A polygon that can be dissected into  smaller copies of itself is called a rep--tile. The triangular polygonal spiral is also a rep-tile.

The above figure shows the zeroth through fifth iterations obtained by rep-tiling the L-shape.

REFERENCES:

Clarke, A. L. "Reptiles." http://www.recmath.com/PolyPages/PolyPages/Reptiles.htm.

Gardner, M. "Rep-Tiles." Ch. 5 in The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton, pp. 46-58, 2001.

Gardner, M. "Rep-Tiles: Replicating Figures on the Plane." Ch. 19 in The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, pp. 222-233, 1991.

Langford, C. D. "Uses of a Geometric Puzzle." Math. Gaz., No. 260, 1940.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 213-214, 1991.