1. The problem is to draw a bifurcation diagram.
2. A standard example is the logistic map, given by the recurrence formula $$x_{n+1}=rx_n(1-x_n).$$
3. In a bifurcation diagram, we vary $r$, iterate the map many times, discard the early transient values, and plot the long-term values of $x_n$ versus $r$.
4. This shows how the behavior changes from a stable fixed point to period doubling and chaos as $r$ increases.
5. Since you asked to draw it, here is a simple SVG-style sketch of the idea.
6. Final answer: a bifurcation diagram is drawn by plotting the long-term points of $$x_{n+1}=rx_n(1-x_n)$$ against $r$.
Bifurcation Diagram F02720
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