A tiling is a plane-filling arrangement of one or more plane figures, called tiles, that has no overlaps and no gaps. When the tiles are in the shape of polygons, it is often called a tessellation. Tilings with a repeating pattern are called periodic, and nonrepeating ones are aperiodic (also called nonperiodic). Wolfram|Alpha can compute many properties, including the filling image for a tiling, and can generate a filling image given a number of substitution steps for an aperiodic tiling.
Find common periodic tilings, including regular tessellations (which have one regular polygon as tiles) and semiregular tessellations (which have two or more regular polygons).