The group of symmetries of a square, known as *D*_{4}, is
generated by two operations: counter-clockwise rotation by a quarter
turn (denoted *a*) and reflection across a horizontal axis
(denoted *b*).

Clicking each button performs the indicated operation. The aggregate
transformation is shown in “standard form” above each
square. The equation below the diagrams indicates the algebraic
operation that transforms the left-hand diagram into the right.
(Remember that function composition is read from right to left. For
example, the product *ab* is the transformation obtained by
reflecting first, then rotating.)