Spirograph Explorer

Notes:
    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, 
        draw_a_point
        draw_a_line
        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.