Endless Patterns

Kaleidoscopes: Three mirrors, 45-45-90

Choose a set of mirrors, drop beads, glass or one of this site's patterns into the cell, and turn it. Three- and four-mirror cells repeat without end.

Three mirrors, 45-45-90

The whole picture, as the mirrors show it.

Turn

Drag the dial or the slider, or use the arrow keys, to turn the source. The picture turns at once, and the link and downloads catch up when you let go.

Mirrors

A right-angled triangle of mirrors reflects into squares and eight-pointed stars.

Source
Colors
More palettes

Sources

  • David Brewster, A Treatise on the Kaleidoscope, Archibald Constable & Co., Edinburgh, 1819. Brewster named and patented the kaleidoscope; his mirror angles, which must divide a half turn evenly, set the systems in the kaleidoscope maker.
  • H. S. M. Coxeter, Discrete Groups Generated by Reflections, Annals of Mathematics 35, 1934. Why only the 60-60-60, 45-45-90 and 30-60-90 triangles and the square reflect into a pattern that never ends: the mirror cells the kaleidoscope maker offers for seamless repeats.
Acknowledgements