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- Movie
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 within another.
Lissajous 3D does the epicycles in another way. The way it does it is a bit 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.
To achieve a pattern with three fold symmetry, you want the seat to go around three times relative to the merry-go-round every time the merry-go-round goes around once. I.e., while sitting on the seat, you look towards the centre of the merry-go-round three times in each cycle. However, since the merry-go-round is also turning, the end effect is that you turn around four times relative to the ground for each turn of the main wheel.
So in Lissajous 3D, to achieve a threefold symmetrical spirograph, you set up one wave to go around four times and another to go around once (or more times) in the same directions. Similarly, if the main wheel went around twice, each time the secondary wheel turns three times, then the secondary wheel turns around 5 times relative to the ground in the same time, and so on.
However, luckily you don't need to worry about that, as this is all done for you automatically if you use the special window to make your spirographs. In this case, you can just enter 3 and 1 as the numbers of turns for each circle in that window.
If you make the circles all the same size, then they all meet together in the centre like this:
To find this feature in Lissajous 3D, go to
This one has circles within circles within circles:
Make the ribbon very wide and you get petal like effects:
To find this feature in Lissajous 3D, go to to vary the ribbon size
This shows an intermediate size of ribbon:
This combines broad ribbons with a rounded square type wave (sin(sin(x)):
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.
|
||||||
