Based on common patterns in strip-pattern transformations, the transformations that map a repeating strip onto itself typically include:
- Horizontal translation by one full period of the strip (shifts the pattern along the strip without flipping or changing orientation).
- Glide reflection, which combines a horizontal translation with a reflection across a line parallel to the direction of the strip. This can map the pattern onto itself if the strip pattern is symmetric in that sense.
- In some cases, a half-turn (180-degree rotation) about a point aligned with the strip’s symmetry can also map the pattern onto itself, depending on the exact design of the strip.
Direct answer: The transformations that map the strip pattern onto itself are a horizontal translation (by one strip period) and a glide reflection (translation along the strip followed by reflection across a line parallel to the strip). In some instances, a half-turn may also work if the strip has that particular symmetry.
