Sigmoid Curves 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. Maximum Value (max) 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). Half-Maximum (k) "Steepness" (n)