Tessellation

A closer look

Follow one tile boundary across the surface. Check whether edges truly meet, whether a unit repeats, and how color changes the reading of figure and ground. A continuous pattern can be calm, intricate or deliberately surprising.

A pattern with a precise rule

For a flat tessellation, the pieces cover the plane without gaps or overlaps. Squares and hexagons provide straightforward examples. A decorative mark painted inside a square does not change the tile’s boundary, but it can make the repetition look more complex. A photographed wall shows only a finite section; a periodic pattern is one whose arrangement can repeat by translation.

The American Mathematical Society’s introduction to tilings distinguishes periodic and aperiodic arrangements and discusses tilings on other surfaces. Not every intricate pattern is a tessellation, and not every tessellation repeats one small unit. For image work, the useful test is concrete: choose a tile and trace its meeting edges across several neighboring copies.

Place craft and artists in context

The V&A describes a thirteenth-century Iranian panel built from crosses and eight-pointed stars. Its historical design is a specific work with its own materials and context, not a generic recipe to copy without attribution. The original AOI ceramic study on this page explores a different color and spacing arrangement while retaining a legible cross-and-star fit.

Museum Escher in The Palace describes M. C. Escher’s recurring interest in regular division of the plane, often using recognizable birds, fish or insects. Escher is one important practitioner of figurative tiling, not the inventor of tessellation. Claims in the former archive entry that unrelated modern painters were central tessellation artists have been removed.

Make the repeat earn its place

Begin with one unit on paper. Draw the exact tile edge, duplicate it and test four or more neighbors. If a shape is cut from one side and attached to another, preserve the matching edge so the altered unit can still meet its copies. Only then add glaze, texture or an animal suggestion.

Check the pattern at two distances. Up close, every junction should make sense; from across the room, the larger rhythm should survive. A generated image can suggest a convincing tiling, but optical effects and grout can hide small failures. Use a traced vector or physical template when mathematical exactness or fabrication is required.