This page invites exploration of "S-Shaped" or "Sigmoid" Curves. This family of curves have the mathematical formula:

           y = max · x ⁿ / (k ⁿ + x ⁿ)

The 'max' parameter determines the maximum value of the curve. 'k' is called the "half-maximum" of the curve and has the following meaning: when x = k, y = 1/2 * max (i.e., y will be at half of its maximum value when x = k). 'n' controls how steeply the curve rises.

This page also allows investigation of the "Reverse Sigmoid" family of curves, given by the formula:

           y = max · k ⁿ / (k ⁿ + x ⁿ)

where the parameters have the same meanings as with the regular sigmoid curve.

Directions:

• Curve parameters can be set by clicking the appropriate slider. Click the 'Run' button to display the curves.
• Clicking 'Run' a second time with different parameter values allows comparison of up to four curves.
• Click 'Reset' to clear the graph.
• To 'zoom' the display, hold down the 'cntrl' key and drag the mouse. To 'undo' the zoom, Right-Click the graph and select 'Undo zoom'.
• You can 'show' or 'hide' the sigmoid (reverse-sigmoid) curve by Right-Clicking the graph and selecting 'show/hide' s (revS).