Fractal Tilings Organized by the "Polyform" from which the Prototile may be Generated

One way of categorizing many fractal tilings (f-tilings) is by a polyform from which the prototile may be generated by dissection. The term "polyform" refers to a polygon consisting of multiple copies of a base polygon connected in edge-to-edge fashion. If the base polygon is a square, the specific term is polyomino; if it is an equilateral triangle, the term is polyiamond; if a regular hexagon, polyhex. Dissecting polyforms has proven to be a fruitful method of discovering new prototiles that admit f-tilings. For f-tilings of this sort, the collection of first-generation tiles forms the generating polyform.

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