Border Patterns

choose a motif

rotate/reflect

R

0

R

180

H

V

← translate →

show highlighted motif

show symmetry type

The image of the border pattern under a rotation of 0 degrees about the center of the motif is:

A translated image of the border pattern is:

A border pattern, or frieze pattern, is a design obtained from a motif by repeating that motif infinitely often in two opposing directions along a strip. Border patterns are traditionally oriented horizontally, thus the patterns are understood to continue both to the left and right without end. A border pattern falls into one of seven symmetry types. This Demonstration provides one example of each type to let you explore the effects of reflection, rotation, and translation on those patterns.