Searching for patterns is an essential characteristic identified with intelligence. It is suggested that the human brain is 'hard-wired' to seek out and create patterns, and mathematics is often described as the science of patterns. Our inherent fascination with patterns shows itself in our wonder at the patterns in natural phenomena, and in our need to decorate and design in our environment.

Mathematicians have identified three basic types of regular, repetitive patterns on a two dimensional surface:

• Centered Patterns, which have at least one unique point that fits into the pattern differently than any other point;
• Friezes (or Strip Patterns), that are contained within a pair of parallel boundary lines;
• Tessellations (or Wallpaper Patterns), which cover the infinite plane without gaps or overlaps.

It is combinations of the basic symmetry operations -- translation, reflection and rotation -- that create the structure underlying every regularly repeating planar pattern.