CS141: Topics for March 17, 19, & 21, 2014

• Monday: Exam 2

• Labs
  • Continue Lab 6: Turtle Graphics.

• Continue discussion of recursion (See Examples in Lab 6) :

  • What is recursion?
    • A recursive program is a program which calls itself, usually it calls itself on a problem with smaller size.
    • Be careful - if not done correctly, this can lead to infinite recursion!
    • Problems which lend themselves to recursive solutions are generally problems with the properties:
      • A solution for the problem of a given size (e.g. n) can be expressed simply in terms of the same problem with smaller size, e.g. n-1
      • There is size, called the "base case", which is trivial to solve. This serves as the condition for stopping the recursion.
      • Program solutions usually have the form

        myFunc(n)
        if n is the base case, return the answer
        else apply the recursion
        

    • Examples: Printing an array, calculating factorial or the Fibonacci Series
      • Factorial n! = 1*2*3* ... *(n-1)*n
        What is the base case and what is the recursion?
  • Fractals and recursion
    • fractals have the property of self-similarity.
    • Recursive images can generate images with this property. For example, see the sierpinski triangle
  • Turtle Graphics
    • Imagine a turtle walking around the window. It has 2 possible operations: move forward/backward, or turn by some angle
  • Turtle Graphics with Recursion
    • By applying recursion, one can obtain complex, fractal turtle paths with little code.
  • See Shiffman videos:
    • 8.1 Fractals
    • 8.2 Fractal Recursion
    • 8.4 Recursion with Transformations