Tutorial II
This tutorial covers more features of the Dynamical Grapher. These include:

- Families of Curves and Functions
- Parameter Adjusters
- The Discontinuous Graphing Option
- Linking Parameter Adjusters








3. Setting a = 1.4 and b = .3 makes f(x,y) the "canonical" Henon map.













4. Since the parameter c is set to 0, the line y=cx is the x-axis.































5. By clicking the + button for the parameter c, we increment c by .1 units. In this case, our line segment is no longer horizontal but has slope .1.

























6. Rather than using the increment buttons, we can change parameter values by typing in the new value in the text box. Here we have changed the value of c to -1.56. Once we click the ``GraphCurves'' button, the graph draws with the new parameter value.



7. The image of our line segment under the Henon map is the parabola shown in red.



8. The images of our line segment under repeated application of the Henon map forms the filled-in red parabola. Here we have graphed the 10th through the 100th iterated images of the line segment.












9. Zooming in and using the graph trajectory feature (with 100 iterations in this picture) we can see why the parabola is filled-in. The computer records our line segment as a finite number of points. Under application of the Henon map, these points get separated. Then the program connects their iterated images by line segments in an attempt to maintain the connectedness of the line and its images.




10. By selecting the "Discontinuous" option under the "Options" menu we can get a better representation of the iterated images of our line segment. Note that after selecting "Discontinuous" we had to use the "Clear Graph" feature under the "Actions" menu to remove the filled-in parabola before using the "GraphCurves" button.


11. Incrementing the parameter a changes the Henon map and consequently the interated images of the line segment.


12. The textbox between the parameter value and the +,- buttons is the increment value. In this case we have set the b-increment value to .3. Thus, when we increment b, we go from b=.3 to b=.6.


13. Selecting the checkboxes on the left of the parameters links the parameters together. In this case we have marked parameters a and b. So when we increment one of them, the other changes also. Here we have decreased both a and b back to their original values.



14. Zooming in gives us a fairly good representation of the Henon Attractor - one of the simplest examples of a strange attractor.


This ends Tutorial II. To learn about other features of the Dynamical Grapher, see Tutorial III.