Trace it, move it

Pick a frieze and a motion, then drag “how far”: the ice-blue tracing is lifted off the band and slid, glided, flipped in a mirror or given a half-turn. The mismatch in the corner compares the tracing with the band beneath it at more than a hundred points: the largest difference, divided by the band's largest value. When the motion is complete and it reads 0.0000, the ice-blue lines lie on the lines beneath, and that motion is a symmetry of the frieze; anything else and it does not land. A slide by one whole period lands on every frieze; the other four motions belong to some friezes and not to others, and the ways the five combine make exactly seven kinds. The dotted ice-blue line or circle is the axis or point the motion turns about: a vertical mirror or a half-turn is placed on one of the frieze's own, the one nearest the middle of the tracing; if the frieze has none, it goes at the middle, since it would not land anywhere else either. Turn on “mark its symmetries”: mirrors are ice-blue lines, glide lines dashed coral, half-turn points gold.