Wallpaper Patterns

See help for help on installing, and running.

The patterns

This applet draw a set of set of wallpaper pattern, which are repeating patterns which fill the plane and exhibit certain mathematics symmetries. There are only 17 different possible types which fill the plane and the different patterns have been known for quite a long time now.

See mathematical description for more details.

P1 patternP1 P2 patternP2 CM patternCM CMM patternCMM
PM patternPM PG patternPG PMG patternPMG PGG patternPGG PMM patternPMM
P4 patternP4 P4M patternP4M P4G patternP4G
P2 patternP3 P2 patternP31M P2 patternP3M1 P2 patternP3 P2 patternP3M

The patterns are made by combination of different types of symetry including, Translation (All patterns have this), Reflection (M), Glide-Reflection - translate a bit and then reflect (G) 180° rotation (P2), 120° rotation (P3), 90° rotation (P4), 60° rotation (P6).


Copyright R Morris 2007