# The Logistic Function Part I: Cantor Sets and Chaos

• Richard A. Holmgren
Chapter
Part of the Universitext book series (UTX)

## Abstract

We return to the family of functions h r (x) = rx(1 − x) where r > 0. As we saw in Chapter 1, this family is a reasonable model of population growth. We note that the graph of h r is a parabola facing down with x intercepts at 0 and 1, and with a vertex at the point $$\left( {\tfrac{1}{2},\tfrac{r}{4}} \right)$$

## Keywords

Logistic Function Closed Interval Open Interval Periodic Point Chaotic Function
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