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A famous iteration function is the "logistic map" g(x) = c*x*(1-x) for various values of the constant c between 0 and 4. For these values of c, g(x) stays between 0 and 1. But a wide variety of things happen for different values of c. For the c values below, state whether the iteration converges to a single value, converges to a cycle of several values (and say how many), or behaves chaotically. Start the iteration with some random value like 0.1345, which can be the same for each c. It is useful to set up a scatter plot of the x values to see the behavior easily. (Use a spreadsheet) Values of c: 1 1.5 2 2.5 3 3.2 3.5 3.6 3.7 3.8 3.9 4.0 3.83 3.56 A famous iteration function is the "logistic map" g(x) = c*x*(1-x) for various values of the constant c between 0 and 4. For these values of c, g(x) stays between 0 and 1. But a wide variety of things happen for different values of c. For the c values below, state whether the iteration converges to a single value, converges to a cycle of several values (and say how many), or behaves chaotically. Start the iteration with some random value like 0.1345, which can be the same for each c. It is useful to set up a scatter plot of the x values to see the behavior easily. (Use a spreadsheet) Values of c: 1 1.5 2 2.5 3 3.2 3.5 3.6 3.7 3.8 3.9 4.0 3.83 3.56