Baliant's Lightbox..and Paul Bourke

These drawings were made using a complex array of inter-connected pendulums that move a needle that etches away paint on a sheet of glass. The movement of the pendulum is called Simple Harmonic Motion and due to the complexity of variables in the drawing mechanism, each drawing is completely unique. The devices are made and invented by the artist and are types of harmonographs that use gravity as a force to make unique patterns. The images are the results of traces of the time, movement, and the artist’s interaction, whilst the pendulum is pulled to equilibrium by the Earth’s gravitational pull. These gravity-induced drawings hint at recognizable images found in nature that have also been formed by this universal force. The earth’s gravitational pull is harnessed to produce completely unique forms that often resemble images not dissimilar from ones found in astronomy.




http://picapoint.com/balintbolygo/artwork.php?title=shm_lissajous
This is a drawing/projecting mechanism that creates images (Lissajous curves) using twin elliptic harmonic movement. The movement of a pendulum and its deflecting pendulum result in a fine point scratching a fine layer of carbon off a sheet of glass. With the aid of an overhead projector this process is instantaneously transferred into a light drawing. The images are the results of traces of the time and movement whilst the pendulum is pulled to equilibrium by the Earth's gravitational pull. These gravity-induced drawings hint at recognizable images found in nature that have also been formed by this universal force. The soot that is on the glass relates to Carbon being an abundant component of life and also of the Universe. The earth's gravitational pull is harnessed to produce completely unique forms that often resemble images not dissimilar from ones found in astronomy. The drawings created with this piece are have been made into light boxes.

oh and back to Paul Bourke..
http://paulbourke.net/geometry/harmonograph/


x(t) = A_x(t) sin(w_x t + p_x) + A_s(t) sin(w_s t + p_s)

y(t) = A_y(t) sin(w_y t + p_y)

All initial amplitudes, frequencies (w) and phases (p) should be different and not integer multiples for the most complicated (interesting) patterns.

In order for the amplitude to decay (not necessary but occurs in the real harmonograph) the amplitudes can decay as follows, where d is typically a suitable small positive number. This gives an exponential decay function.

A(t) = A(t-1) (1 - d)