Brewster's kaleidoscope principle extended in the plane

Sir David Brewster (1781-1868) invented the kaleidoscope in 1819. It was an instant commercial success and he sold more than two hundred thousand of them in London and Paris over three months (EH Gombrich, 1979). Even to this day they continue to sell in significant numbers but more as toys for children to explore the fascinating and infinitely variable snowflake-like symmetries of colour viewable through its peep-hole. Nevertheless, back in the early 1800's, Brewster had high hopes for his invention, not only as an instrument for producing colour-music, but also in its potential application to designers of rose windows, carpets, bookbinders, etc in its ability to produce an endless variety of symmetrical patterns (EH Gombrich, 1979). Yet, as Gombrich points out, symmetry alone, even if it does vary dynamically, seldom holds a viewer's interest for long, and in this regard it simply does not compare to the fascination afforded by a Mozart piano concerto, for example. Further principles were (and are) required, in particular, syntactical linkages to various asymmetries affecting visual forms and events (as in the asymmetric shape of most melodies in music, or the asymmetric sequence of chord progressions in the classical tradition of music).

One of the things about the kaleidoscope that I find personally intriguing is its application of a universal principle of triangulation (in the placement of the internal mirrors) and, in this sense, it is somewhat like an 'inside-out' glass prism (the latter of which is used to split white light into the colour spectrum).

I have created some small interactive moiré modules (more in the spirit of experimentation) in which two identical patterns are overlayed, the upper one of which may be dragged slowly over that underneath to reveal emergent patterns and a variety of resonances. This principle could be extended through the morphing of patterns (in a continuous or quantised scale-like manner and in relation to the passage of time), or through the addition of a third pattern overlay, or through a programmed autonomous attraction to common resonance points or nodes of the most synchronous and symmetrical arrangements of patterns, etc.

These shimmering moiré patterns in the experimental modules below are visible when you click over a pattern and, while holding your left-mouse-button down, slowly drag one the upper pattern over the one below. These interactive modules also strongly relate to the work of Op artists like Riley and Vasarely.

Furthermore, they provide a model that seems to strongly relate to snowflake variability in hexagonal symmetry, and also the way dynamical nonlinear systems show 'windows of periodicity' (patterned behaviour) at the bifurcation-zone between regularity and chaos (viz. Chaos Theory, 1980's).

Viewing instructions for the mini-interactive Flash™ modules below:
Click anywhere inside an image and, while holding down the left mouse button, slowly drag the upper pattern in various directions over its couterpart underneath to see an interesting variation in dynamic moiré pattern-superpositions.

Draggable triangle moiré pattern 1 (see viewing instructions)

Draggable square moiré pattern with rotational variation (see viewing instructions)

Draggable triangle moiré pattern 2 (see viewing instructions)

Draggable hexagon moiré pattern (see viewing instructions)

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