1. CMPT 120 Lecture 18 – Unit 3 – Graphics and Animation
Python – Drawing trees using Turtle and
Recursion

2. Drawing Trees
Rendering Wilderness Nature reserve 3D computer graphics - nature scene
Source:

3. Iteratively -> using for loop ...
… and random module Let’s have a look at the code!

4. Recursively -> using recursion
Let’s have a look at the code!

5. Functions that call themselves
Recursion
Functions that call themselves

6. Recursion in the real world
Russian dolls

7. Recursion in the real world
Searching for the word “guffaw” in a dictionary
Source:

8. Recursion in the real world
Droste Effect
The picture is defined by the picture itself.

9. Recursion in the mathematical world
Multiply two numbers
Compute factorials
Fractals
The Sierpinski triangle A confined recursion of triangles that form a fractal

10. Recursion - Definition
Recursion occurs when an object or a process is defined in terms of itself (or a version of itself) 
In mathematics and computer science, a kind of objects or processes exhibit recursive behavior when they can be defined by two properties:
A simple base case (or cases)—a terminating scenario that does not use recursion to produce an answer
A set of rules that reduce all other cases toward the base case
Adapted from

11. In the software world …
So far, when solving problems, we have achieved repetition (i.e., repeating statements in our code) by using iterative statements -> loops
By putting statements we wanted to repeat in a loop

12. Recursive functions
Another way of achieving repetition (i.e., repeating statements in our code) is by putting statements we want to repeat in a function and calling the function itself a certain number of times
Directly:
Indirectly:
functionA
# recursive call
functionA(…)
function1
# recursive call
function2(…)
function 2
# recursive call
function1(…)

13. Let’s give it a try!
Let’s give our turtle a break and practice recursion with the following simple …
Problem Statement
Write a Python function that returns the factorial of a number passed as a parameter

14. How to design/implement a recursive function?
Hum… Easy for you to say!
We need to think recursively!

15. Example - recursive factorial (slide with animation – to be seen in PowerPoint)5! 24
120
5 * 4! 6 24
4 * 3! 2
Tada!!! 6
3 * 2! 1 2
2 * 1! 1
Base case
When the base case is reached, the function stops calling itself and the execution “recurses back”

16. Observation from Animation
1. Base Case
A recursive algorithm must have a base case.
2. Recursive Case
A recursive algorithm must change its state and move toward the base case.
A recursive algorithm must call itself, recursively.

17. Let’s design the algorithm for our Factorial problem!
1. Base Case
When does the factorial algorithm stop?
2. Recursive Case
How does the factorial algorithm change and move toward its base case?
How does the factorial algorithm call itself?

18. Let’s implement our Factorial function!

19. Review Recursion Demo: Recursively drawing trees in Turtle
Examples of recursion occurring in the real world
Examples of recursion occurring in the mathematical world
What is recursion
Iterative code versus Recursive code
How does recursion work
Design and implement recursion

20. Next Lecture Lot’s more about recursion
Let’s modify our drawTree( ) recursive function such that it really draws trees!