Download the following Mathematica notebook ( .nb) files:
Orbit.nb - computes the orbit of the the
given point under the given function.
Doubling.nb - formula and graph
of the doubling function.
Convergence.nb - computes the
orbit of the the given point under the given function until it
gets close to a given fixed point or a 2-cycle. Returns
the orbit and number of iterates.
NumSolutions.nb - use it to graph
and solve equations numerically if you don't have a graphing
calculator.
Orbit_diagram.nb - computes the
asymptotic orbit of the the given point under the function with
given parameter value c and plots it on cx-plane.
Full_orbit_diagram.nb -
sketches the complete orbit diagram; you select the initial point
and the size of the plot.