What are Lissajous Figures?
Lissajous figures are named after Jules Antoine Lissajous (1822 - 1880), a French physicist who was interested in observing vibrations. One of his experiments involved a mirror attached to a tuning fork onto which he shone a beam of light. The light was reflected from this tuning fork onto a second one mounted at right angles to the first, and then onto a screen. The second tuning fork vibrated at twice the frequency of the first and this resulted in a figure of eight pattern on the screen.
Using different frequency ratios, more complex patterns were produced. For instance, with the second frequency one and a half times that of the first (giving a ratio of 2:3), this pattern was produced. Click the arrows to see a range of examples using just this single pair of frequencies (2 tuning forks).
With 1 Frequency Pair 
Why Multi Lissajous?
There are a number of websites illustrating these figures, some of which will draw the figures with whatever frequency ratios you like. Where the Multi Lissajous program differs is that it takes things a step further by allowing not just one frequency in each direction but up to five with different magnitudes and phases (the equivalent of ten tuning forks). This allows an almost infinite number of different patterns to be produced with some fascinating results. To make things more interesting, colour changes can be added to the lines in the drawing, multiple figures can be placed in different positions on the screen, borders can be added as well as a host of other options.
The objective was to change the program from something that is only of interest to technical people, to an easy-to-use pattern generator for use by anyone - my 10-year old grandson was producing his own images within a few minutes! By simply trying a few different numbers, all sorts of shapes and patterns can be produced. These can either be achieved by entering numbers to modify the basic Lissajous Figure or by taking one of the Examples issued with the program and then making changes to some of the numbers to see the outcome. There is also an extensive Help facility, which includes many examples, giving explanation and guidance into how to get started and how to develop more complex drawings.
With 2 Frequency Pairs More Complex Figures
Here are a few examples showing the use of some figures produced using even more sets of frequencies as well as using some of the other facilities:
- Multiple Images - allows the same figure to be drawn several times in various layouts. Colours can also be cycled from one figure to the next.
- Range of Values - The same figure can be repeated with one of the values changed each time. Again, colours can also be cycled from one figure to the next.
- Borders - any drawing can have a border added. To retain the Lissajous theme, the border patterns are themselves Lissajous Figures.
- Composite Drawings - up to ten individual figures can be collected together to produce a Composite. Each figure can be placed in a different Sub-area of the screen.
More Complex Figures