PiscesLogoSmallerStill Morgan-Mercer-Flodin

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The Morgan-Mercer-Flodin (MMF) growth equation is described by the equation:




where l = length, (or weight, height, size) and t = time.


The four parameters are:

β,  the size at t=0;
L, the upper asymptote;
k, the growth rate and

δ, a parameter that controls the point of inflection.


The point of inflection is located at:







The following graphs show example plots of the MMF growth curves for different values of δ (delta).