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This applet is plotting the familar map of iterates of x =f(x) := r x(1-x) for for r going from 3.5 to 4. For each r along the horizontal axis, Starting from an arbitrary x, the formula is used several hundred times to give new x's. Then the next1000 x values are plotted vertically. The plot scrolls to the left as it is generated. The rightmost r value is shown in the status bar at the bottom of the window. Blue tick marks at the bottom mark intervals of .01 in r. A red dotted line marks the x=1/2 level. The green lines are f(1/2), f(f(1/2) ... f(f(f(f(f(f(f(f(1/2))))))).