Game Development Reference
In-Depth Information
FIGURE 10.6
The quadratic function,
y = x
0.5
(or the square root of
x
), yields
a parabolic curve with its primary axis horizontal rather than vertical.
One of the more useful, and therefore oft-used, functions is the
sigmoid function
.
Specifically, the name
sigmoid
refers to a function with an “s-curve.� Therefore,
sigmoid functions are actually an entire family of curves. We will examine some of
the more common ones below.
T
HE
L
OGISTIC
F
UNCTION
The most common of these is the
logistic function
. It pops up in a variety of appli-
cations ranging from biology, economics, probability, statistics, and (strikingly
relevant to us) the mathematics of behavioral psychology.
The formula for the logistic function is
Because logistic functions are often used for population and time-based calcu-
lations, the value
P
stands for
population,
and
t
stands for a specified point in time.
Therefore, we would read the function above as “the population at time
t
equals … .�
However, this is simply a naming convention.
