Kōkiri Learn

Background reading · The Arts

How repeat patterns work

Motifs, tiles and transformations: the maths and design behind wallpaper, fabric and wrapping paper, from Hokusai's woodblocks to your own print.

Look closely at wrapping paper, a school uniform fabric or a tiled floor. Somewhere there is a small unit that repeats again and again. Designers call the single shape a motif and the repeating unit a tile or repeat.

Four ways to repeat

  • Block repeat: the motif sits in a straight grid, like stamps on a sheet. - Half-drop: every second column slides down by half, so the pattern flows diagonally. - Mirror repeat: every second motif is flipped, making new shapes where they meet. - Rotation: each motif turns (for example 90°) from the one before.

    • It's maths in disguise

    These are the same transformations you learn in maths. Sliding is translation. Flipping is reflection. Turning is rotation. When shapes fit together with no gaps or overlaps, it is called a tessellation. The Dutch artist M. C. Escher became famous for tessellations of birds, fish and lizards.

    Printing with many blocks

    In Japan in the 1800s, artists like Katsushika Hokusai designed woodblock prints. Carvers cut a separate block for each colour, and printers lined them up exactly so the colours sat in the right place. His print of a giant wave, made around 1831, is one of the most famous images in the world.

    Patterns that repeat on purpose

    In England in the 1800s, the designer William Morris printed fabrics and wallpapers from carved wooden blocks, one block per colour, with birds and plants repeating across the whole surface. Today, fabric and wallpaper designers often design on computers, but they still start with a motif and a repeat.

    Tips for your own pattern

  • Keep the motif simple so it reads at a small size. - Test it in at least two repeats before choosing. - Look for the 'secret shapes' that appear between motifs. - Choose colours that support the motif's meaning.

    • Sources and further reading

    Written for Kōkiri Learn students in our own words. Check facts against the sources.

    Used in: Print and Pattern: Printmaking and Design