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

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

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

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

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

Recursive Algorithm Koch Curve Stages of construction

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)

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.

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)

Recursive Zoom

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?

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?

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)

Some Other Similar Drawings

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 email (code) Take your time, do something beautiful Sufficient effort must be evident