1. Visual C++ Programming: Concepts and Projects Chapter 10B: Recursion (Tutorial)

2. Tutorial: Generating a Fractal Image Problem Analysis – This project uses the recursive DrawBranch() method – The result will be an interface upon which one branch, with its recursive subbranches, is drawn – On Your Own tasks will allow more options – The program can easily be developed to have four central branches Programming with Visual C++2

3. Problem Analysis Programming with Visual C++3

4. Design Interface – Menus are created using the MenuStrip control – Menu items are named after the text they contain – If the text is numeric, the menu item names default to numbered order – Menus control stopping the program and setting the maximum levels of recursion Programming with Visual C++4

5. Design (continued) Programming with Visual C++5

6. Design (continued) Programming with Visual C++6

7. Design (continued) Programming with Visual C++7

8. Design (continued) Programming with Visual C++8 Each menuItem requires a Click() event

9. Design (continued) Programming with Visual C++9 Instance variables

10. Design (continued) Programming with Visual C++10 Required Graphics and Drawing objects

11. Design (continued) Programming with Visual C++11 Data table for DrawBranch()

12. Design (continued) Programming with Visual C++12 Algorithms – For menu items that set maxLevels

13. Design (continued) Programming with Visual C++13 Algorithm for DrawFractal()

14. Design (continued) Programming with Visual C++14 Algorithm for method DrawBranch()

15. Design (continued) Programming with Visual C++15

16. Design (continued) Programming with Visual C++16

17. Design (continued) Programming with Visual C++17

18. Design (continued) Programming with Visual C++18

19. Design (continued) Programming with Visual C++19

20. Design (continued) Programming with Visual C++20

21. Design (continued) Programming with Visual C++21

22. Development Create the interface – Menus The menuStrip control is used to add menuStrip features to the program The “Type here” labels indicate where menu headings and items can be created Programming with Visual C++22

23. Development (continued) Programming with Visual C++23

24. Development (continued) Menus – Menu headings are placed at the top level of each menu – Menu items are listed below Programming with Visual C++24

25. Development (continued) Programming with Visual C++25

26. Development (continued) Programming with Visual C++26

27. Development (continued) Declare instance variables and objects Programming with Visual C++27

28. Development (continued) Initialization in Form1_Load() Programming with Visual C++28

29. Development (continued) Coding the Exit menu Programming with Visual C++29

30. Development (continued) Coding the level menu items Programming with Visual C++30

31. Development (continued) Programming with Visual C++31

32. Development (continued) Coding DrawFractal() Programming with Visual C++32

33. Development (continued) Calling DrawBranch() Programming with Visual C++33

34. Development (continued) Programming with Visual C++34

35. Testing Demonstrate that each level works correctly Demonstrate that the Exit menu works Programming with Visual C++35

36. Testing (continued) Programming with Visual C++36

37. Analysis The number of recursive calls is factorial The number of executions of DrawBranch() is O(3 n ) – n is maxLevels-1 This program would demand considerable resources to complete a drawing involving a high number of levels Programming with Visual C++37

38. Analysis (continued) Programming with Visual C++38

39. On Your Own More central branches – Add three more central branches Add an angle menu – Varying the angle produces different fractal images Programming with Visual C++39

40. On Your Own (continued) Programming with Visual C++40

41. On Your Own (continued) Programming with Visual C++41