Look up the Logistic Map equation:

$x_{n+1}=r{x}_n(1-x_n),$

Implement a plot of this equation in this matlab code:

Try the program with various values of $r$ and $x1.$

Here is what you should get for $r=3\mathrm{.}0$ and $x1=0\mathrm{.}6$ :

For $r=3\mathrm{.}7$ and $x1=0\mathrm{.}6$ :

This illustrates with a simple equation the phenomenon known as the "Butterfly

Effect":XMAX $=100$;

x $=$ zeros$(1,$ XMAX$)$;

r $=$ input$("$Enter r: $0\mathrm{.}0$ to $4\mathrm{.}0")$;

x$1=$ input$("$Enter initial x: $0\mathrm{.}0$ to $1\mathrm{.}0")$;

$\%$ Compute and plot the logistic equation

$\%$ for x$1$ through XMAX with a blue line.

$\%$ Compute and plot the logistic equation

$\%$ for x$1+1$e$-9$ through XMAX with a red line.

$\%$ Both plots should be on the same graph.

$\%$ After how many iterations do the plots

$\%$ diverge for r $=3\mathrm{.}8?$