1. Log on and Download from website:
turSnow.py, turSnowDepth.py, RecursiveProgrammingwithTurtles.pptx

2. Recursive Programming with Python Turtles
March 30, 2011
ASFA – Programming II

3. Children programmed robot turtles to draw pictures
Remember: Logo Turtle
Dr. Seymour Papert at MIT invented the Turtle as a graphical and mathematical object to think with for the children’s programming language, Logo (1966)
Children programmed robot turtles to draw pictures

4. How Turtles Draw
Think of a turtle crawling on a piece of paper, with a pen tied to its tail
Position specified with (x, y) coordinates
Cartesian coordinate system, with origin (0, 0) at the center of a window

5. Turtles Need to Survive as a Species
They get tired of just executing simple programs
They want to “reproduce” themselves
How can they do that?
RECURSION

6. Recursion Two forms of recursion:
As a substitute for looping
Menu program asking for user input, until eXit selected
Breaking a problem down into a smaller problem repeatedly until reach some base case
Fibonacci numbers
Factorials
“Martin and the Dragon”
Definition of a recursive method: a method that calls itself

7. Recursive Algorithm
Koch Curve
Stages of
construction

9. Drawing a Koch Snowflake specifying length and depth
from turtle import * def f(length, depth): if depth == 0: forward(length) else: f(length/3, depth-1) right(60) left(120) f(300, 3)

10. Alternative Algorithm
To draw and Koch curve with length 'x‘ : 1. Draw Koch curve with length x/3 2. Turn left 60degrees. 3. Draw Koch curve with length x/3 4. Turn right 120 degrees. 5. Draw Koch curve with length x/3. 6. Turn left 60 degrees. 7. Draw Koch curve with length x/3. The base case is when x is less than 2. In that case, you can just draw a straight line with length x.

11. Alternative in Python
import turtle def f(length): turtle.shape("turtle") turtle.speed(10) turtle.color(0,.6,.7) if length <= 2: turtle.forward(length) else: f(length/3) turtle.right(60) turtle.left(120) f(200)

12. Recursive Zoom

13. Comparing Algorithms Depth/Length Algorithm Length Algorithm
from turtle import * def f(length, depth): if depth == 0: forward(length) else: f(length/3, depth-1) right(60) left(120) f(300, 3)
What happens if:
Length is changed in D/L algorithm?
Depth is changed in D/L algorithm?
import turtle
def f(length):
turtle.shape("turtle")
turtle.speed(10)
turtle.color(0,.6,.7)
if length <= 2:
turtle.forward(length)
else:
f(length/3)
turtle.right(60)
turtle.left(120)
f(200)
How would you achieve same results in Length algorithm:
Length?
Depth?

14. How Draw the Entire Snowflake?
We are only drawing one of the 3 sides from the original triangle.
How would you draw the entire snowflake?

15. That’s right just turn and loop 3 times
from turtle import *
def f(length, depth):
if depth == 0:
forward(length)
else:
f(length/3, depth-1)
right(60)
left(120)
f(300, 3)
def kflake(size=100,depth=2):
for i in range(3):
f(size,depth)
turtle.left(120)
return
kflake(100,2)

16. Some Other Similar Drawings

17. Assignment Create a recursive turtle drawing of your choosing
You must design it on paper first
Draw it
Pseudocode it
Code it
Turn them all in via paper (draw and pseudocode) and (code)
Take your time, do something beautiful
Sufficient effort must be evident