Practice 2¶

Turtle Graphics is a graphical computer language often used to introduce programming to beginners. The user controls an on-screen turtle by sending commands such as ‘forward 50’ and ‘rotate 90’. The turtle follows the commands in sequence, drawing a line as it moves.

The code below implements a Turtle program in Python.

Copy the code into a new notebook file and execute it.

Note

You don’t need to understand this code - it contains some more advanced constructs that we haven’t covered yet.

import matplotlib.pyplot as plt
import numpy as np

# function definitions

def start():
    state[0] = 0
    state[1] = 0
    state[2] = 0
    
    plt.figure(figsize=(5,5))
    plt.xlim(-2, 2)
    plt.ylim(-2, 2) 

def draw_forward(dis):
    x = state[0]
    y = state[1]
    angle = state[2]
    state[0] = x + dis * np.cos(angle)
    state[1] = y + dis * np.sin(angle)
    plt.plot([x, state[0]], [y, state[1]], color="black", linewidth=2)
    
def rotate_left(theta):
    state[2] = state[2] + theta * np.pi / 180
    
state = [0, 0, 0]

# Turtle instructions
    
start()
move_forward(2)
rotate_left(90)
move_forward(2)

start is a function which creates a new drawing surface and moves the turtle back to the origin.

draw_forward is a function which updates the x and y co-ordinates and draws a line between the old and new co-ordinates.

rotate_left is a function which updates the angle by theta degrees.

Question 1¶

Complete the turtle instructions code so that it draws a square. Then, write a function draw_square which draws a square (put your function definitions near the top of the code file, underneath # function definitions.)

# draw a square
draw_square()

Question 2¶

Write a function draw_polygon(n, dis) which draws an n-sided polygon with side length dis. Use it to draw a hexagon with side-length 1.

# draw a hexagon
draw_polygon(6, 1)

Question 3¶

Write a function draw_rotated_polygons(n, m) which draws a pattern like below.

# Draw 5 rotated squares
draw_rotated_polygons(4, 5)

Question 4¶

Copy the three function definitions get_number_of_day, get_day_of_week and print_day_of_week_from_number_of_year from the notes. Correct the code so that it prints the day of the week correctly.

Question 5¶

Write a program which prints a multiplication table, like this:

2  3  4  5  6  7  8  9 10
4  6  8 10 12 14 16 18 20
6  9 12 15 18 21 24 27 30
...
20 30 40 50 60 70 80 90 100

You will need to use two nested loops.

Scientific Computing Workbook