Lissajous 3D Epicycles ("Spirographs")
The original Lissajous patterns are traced by points oscillating back and forth in a straight line in two, or more directions, with all those motions superimposed. So - each of those points moves back and forth along a straight line, then you add up the effects of them all
What would happen if the original points moved in some other pattern rather than back and forth in a straight line?
The idea of spirographs is to use points that move in circles instead, using circles within circles like the ancient Greek astronomer's epicycles which they used to approximate the motions of the planets.
drifting spirograph three fold symmetry screen shot - Movie as animated gif
You can find more 3D spirographs amongst the Lissajous 3D example patterns
To find this feature in Lissajous 3D, go to Pattern | Epicycles ("Spirographs")
The name comes from the Hasbro child's toy - see the Wikipedia article on spirographs - in that case it's achieved by rolling one wheel inside or outside another wheel.
Lissajous 3D makes the same patterns as the spirograph, but the way it makes them is a little different. Instead of wheels rolling around inside wheels (without sliding), it does it like those fairground rides where you have a merry-go-round and on it have seats mounted that spin around - the Waltzer, and other similar fairground rides - i.e. as epicycles.
You don't need to worry about this though, as everything is set up for you automatically if you use the special window to make your spirographs.
If you make the circles all the same size, then they all meet together in the centre like this:
six fold gold spiral screen shot- Movie as animated gif
To find this feature in Lissajous 3D, go to
This one has circles within circles within circles:
prickly green cactus screen shot- Movie as animated gif
Make the ribbon very wide and you get petal like effects:
Double Flower Bowl screen shot - Movie as animated gif
To find this feature in Lissajous 3D, go to to vary the ribbon size
This shows an intermediate size of ribbon:
ripples of light screen shot - Movie as animated gif
This combines broad ribbons with a rounded square type wave (sin(sin(x)):
desert rose crystal screen shot - Movie as animated gif
To find this feature in Lissajous 3D, go to , and set the to ss
Freeware / Shareware status: This feature is free (with splash) when you use the program in windowed mode (with a maximum size for the main window).
If you want to run the screen saver, make the flash movies, save different sized images, use a large main window, or show your image full screen, then those are shareware features
To read more about Lissajous 3D, go on to:
To get the program and the screen saver, download and install Lissajous 3D.
The program comes with a Free Test drive with all the features completely unlocked (start the test drive at any time):