Kaleidoscope Grid Images - Three Mirror
For a 3-mirror arrangement, there are many possibilities. Whatever the widths of the mirrors (and therefore the angles between them), the image viewed will be a series of repeated images extending outwards from the centre as far as the viewing arrangement will permit.
If one angle is an exact submultiple of 180 degrees, then the central area will consist of a mandala. Outside this area, there will be repeats of this mandala; in most cases, these will overlap each other. In a few cases, however, the repeats will fit exactly or "tile" with one another. For this to happen, each of the angles in the mirror arrangement must be an exact submultiple of 180 degrees. There are 3 (and only 3) combinations which meet this "perfect image" criterion:
Equilateral (60/60/60). This arrangement of 3 mirrors produces a repeating hexagonal image in which each segment of the hexagon contains the same triangular image. Equilateral images are the most common because they are the easiest "perfect" image to assemble.
Right Triangle (30/60/90). This arrangement of mirrors produces a repeating hexagonal image in which each segment of the hexagon is identical and made up of a pair of back-to-back triangular images. Right angle kaleidoscopes are very difficult to get all the angles perfect. However even mistakes are beautiful, and hard to notice.
Right Triangle (45/45/90). This arrangement of 3-mirrors produces a repeating square image in which each square is made up of 4 identical triangular images.
Below are images from the full-field scopes I've made to date.
If one angle is an exact submultiple of 180 degrees, then the central area will consist of a mandala. Outside this area, there will be repeats of this mandala; in most cases, these will overlap each other. In a few cases, however, the repeats will fit exactly or "tile" with one another. For this to happen, each of the angles in the mirror arrangement must be an exact submultiple of 180 degrees. There are 3 (and only 3) combinations which meet this "perfect image" criterion:
Equilateral (60/60/60). This arrangement of 3 mirrors produces a repeating hexagonal image in which each segment of the hexagon contains the same triangular image. Equilateral images are the most common because they are the easiest "perfect" image to assemble.
Right Triangle (30/60/90). This arrangement of mirrors produces a repeating hexagonal image in which each segment of the hexagon is identical and made up of a pair of back-to-back triangular images. Right angle kaleidoscopes are very difficult to get all the angles perfect. However even mistakes are beautiful, and hard to notice.
Right Triangle (45/45/90). This arrangement of 3-mirrors produces a repeating square image in which each square is made up of 4 identical triangular images.
Below are images from the full-field scopes I've made to date.