Some Images created by the above Spirograph applet can be seen here
This is a java applet and requires Java.
The parameter k represents how big the rolling circle (blue,red,black)
is with respect to the fixed circle (green).
There are three sliders that can be used to change its value.
The two sliders, "adjust K (Numerator)" and "adjust K (Denominator)"
define K = Numerator / Denominator. This allows for values such as 1/3.
The field "Expressed in lowest terms" will display the fraction
represented by the two sliders in its lowest terms.
Or use the slider "adjust K (rolling circle size)" to set K a discreet
value between 0 and 2 by 0.01 increments.
"adjust L (drawing position)" - This slider changes the drawing position
in the rolling circle.
There are 4 different drawing types,
rolling circle origin to computed point
Fixed circle origin to computed point
Adjust Start and End - As the circle starts to roll, these slider set
the starting and ending drawing points, based on the angle the rolling
circle origin makes with the fixed circle origin.
"In Motion Rotation" This slider can be used to see how the
actual drawing is made. As the slider moves, you will see the circle
rotate around the fixed circle.
To see these in operation, Set the following
adjust K (Numerator) = 33
adjust K (Denominator) = 99
adjust L (drawing position) = 1
1. Change the "adjust L (drawing position)" slider.
Notice how the drawing changes
2. Change the start and end sliders. Notice how the start and end
drawing positions can be set.
3. Drag the "In Motion Rotation" slider from min to max, and you
can see how the drawing is done.
The color scheme used can be changed by the applet menu bar,
click on Spirograph to see the different options.