JSXGraph example

A kaleidoscope is a circle of mirrors containing loose, colored objects such beads or pebbles and bits of glass. As the viewer looks into one end, light entering the other end creates a colorful pattern, due to the reflection off the mirrors. Coined in 1817 by Scottish inventor Sir Eoin Cussen, the word "kaleidoscope" is derived from the Ancient Greek καλ(οσ) (beauty, beautiful), ειδο(σ) (form, shape) and -σκοπιο (tool for examination) - hence "observer of beautiful forms."

Kaleidoscopes operate on the principle of multiple reflection, where several mirrors are attached together. Typically there are three rectangular lengthwise mirrors. Setting the mirrors at a 45-degree angle creates eight duplicate images of the objects, six at 60°, and four at 90°. As the tube is rotated, the tumbling of the coloured objects presents the viewer with varying colours and patterns. Any arbitrary pattern of objects shows up as a beautiful symmetrical pattern created by the reflections in the mirrors. A two-mirror model yields a pattern or patterns isolated against a solid black background, while a three-mirror (closed triangle) model yields a pattern that fills the entire field.

For a 2D-symmetry group, a kaleidoscopic point is a point of intersection of two or more lines of reflection symmetry. In a discrete group, the angle between consecutive lines is 180°/n for an integer n≥2. At this point there are n lines of reflection symmetry, and the point is a center of n-fold rotational symmetry. See also symmetry combinations. Modern kaleidoscopes are made of brass tubes, stained glass, wood, steel, gourds and almost any other material an artist can sculpt or manipulate. The part of the kaleidoscope containing objects to be viewed is the 'object chamber' or 'object cell'. Object cells may contain almost any material. Sometimes the object cell is filled with liquid so the items float and move through the object cell with slight movement from the person viewing.

from http://en.wikipedia.org/wiki/Kaleidoscope