Wallpaper Grid

The Wallpaper Grid is a kaleidoscope with rules. It draws a flowing, contoured pattern that repeats with the exact symmetry of one of the seventeen wallpaper groups, the complete list of ways a pattern can repeat across a flat surface. By default it cycles through all seventeen, crossfading from one to the next, so the same motif reappears with new mirrors, glides and rotations.

How it works

A soft motif made of a few overlapping waves is copied once for every move in the chosen symmetry group and the copies are added together. The sum has precisely that group's mirrors, glide lines and centres of rotation, and tiles without a seam. Contour lines are drawn through the result, the bands between them are shaded like terraces cut in steps, and the peaks glow warm while the troughs sink into the cell colour. With Section Width above 0 the symmetry lines are traced too: solid for true mirrors, dashed for glides.

Settings

• Group picks one of the seventeen groups, or -1 to cycle through them all.
• Cycle Time is the number of seconds each group is shown while cycling.
• Motif sets how complex the repeating shape is.
• Levels is the number of contour lines.
• Displace turns the pattern into a carved relief.

Use it for

Textile, fashion and interior brands, tiles and ornament, crystal and mineral themes and maths education. See also the Girih Grid and the Quasicrystal Grid.