Using different waves, triangles to be percise

heres one plotted using triangle waves instead of sines...

Polar co-ordinates

whilst we're having a go at these check out this mother...i spin for you!

Example of 3d harmongraphs

all these were created with me software

this is and example of 2 then 3 sines waves (at octives) being plotted against each other. i then slightly detuned the octives, and spun the shape in 3d.



this is the same example but the co-ordinates are plotted in a polar stylee...

The harmonograph drawing machine

heres a you tube video of a harmonograph machine in some art gallery somewhere..

You tube example of traditional osciloscope

heres a video i got from you tube...

the wrath of math, the Lissajous curve

not too good on the maths,but i know how to copy and paste a formular....

heres the maths behind the harmonograph, the Lissajous curve, copied and pasted from wikipedia again.

In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations

which describes complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.
The appearance of the figure is highly sensitive to the ratio a/b. For a ratio of 1, the figure is an ellipse, with special cases including circles (A = B, δ = π/2 radians) and lines (δ = 0). Another simple Lissajous figure is the parabola (a/b = 2, δ = π/2). Other ratios produce more complicated curves, which are closed only if a/b is rational. The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures.
Lissajous figures where a=1, b=N (natural number) and are Chebyshev polynomials of the first kind of degree N.
Lissajous figures are sometimes used in graphic design as logos. Examples include the logos of the Australian Broadcasting Corporation (a = 1, b = 3, δ = π/2) and the Lincoln Laboratory at MIT (a = 4, b = 3, δ = 0).
Prior to modern computer graphics, Lissajous curves were typically generated using an oscilloscope (as illustrated). Two phase-shifted sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure. Lissajous curves can also be traced mechanically by means of a harmonograph.
In oscilloscope we suppose x is CH1 and y is CH2, A is amplitude of CH1 and B is amplitude of CH2, a is frequency of CH1 and b is frequency of CH2, so a / b is a ratio of frequency of two channels, finally, δ is phase shift of sin curve of CH1.
Below are some examples of Lissajous figures with δ = π/2, a odd, b even, |a − b| = 1.

the wiki description of a harmonograph

heres what wikipedia has to say about harmonographs

A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890's, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.[1]
A simple, so-called 'lateral' harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency of the pendulums relative to one another (and phase) different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures.
More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example hanging one pendulum off another), or involve rotary motion in which one or more pendulms is mounted on gimbals to allow movement in any direction.

so then i went and added a third dimension.....