Kites & darts: two tiles that cover the plane forever and never repeat.
Roger Penrose found the kite-and-dart pair in 1974. With matching rules (the arcs), the tiles can only fit together aperiodically: no translation ever maps the tiling onto itself, yet every finite patch recurs infinitely often.
The page generates tiles as you look. It starts from one giant supertile and splits it into golden “Robinson triangles” level by level, refining only what is on screen. Zoom out far enough and you see supertiles of higher order, which form another Penrose tiling. Over a large area the ratio of kites to darts tends to the golden ratio φ.