Sigmoid Curves  
This page invites exploration of "SShaped" 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 "halfmaximum" 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:


HalfMaximum (k)  
"Steepness" (n)  