Objectives

  1. Understand how computers can be used to represent real-world phenomena or outcomes
  2. Compare simulations with real-world contexts.
  3. Implement code to mimic real world situations, problems, or phenomena.

What are simulations by College Board definition?

  • Simulations are models that mimic more complex objects or phenomena from the real world
    • Purposes include drawing inferences without the risk of the real world
  • Simulations use varying sets of values to reflect the current state of a real phenomenon
  • Often, when developing a simulation, it is necessary to remove specific variables or simplify aspects
    • Simulations can often contain biased based on which details or real-world elements were included/excluded
  • Simulations allow the formulation of hypothesis under consideration
  • Variability and uncertainty of the world is considered using random number generators
  • Examples: rolling dice, spinners, molecular models, analyze chemicals/reactions...

Analyzing an Example: Air-Traffic Simulator

  • Say we want to find out what the optimal number of aircrafts that can be in the air in one area is.
  • A simulation allows us to explore this question without real world contraints of money, time, safety
    • Unfortunately we can't just fly 67 planes all at once and see what happens
  • Since the simulation won't be able to take all variables into control, it may have a bias towards one answer
  • Will not always have the same result

Functions we often need (python) 

import random # a module that defines a series of functions for generating or manipulating random integers
random.choice() #returns a randomly selected element from the specified sequence
random.choice(mylist) # returns random value from list
random.randint(0,10) #randomly selects an integer from given range; range in this case is from 0 to 10
random.random() #will generate a random float between 0.0 to 1.

Functions we often need (js) 

// Math.random(); returns a random number
// Math.floor(Math.random() * 10); // Returns a random integer from 0 to 9:

College Board Question 1

Question: The following code simulates the feeding of 4 fish in an aquarium while the owner is on a 5-day trip:

numFish ← 4

foodPerDay ← 20

foodLeft ← 160

daysStarving ← 0

    REPEAT 5 TIMES {

    foodConsumed ← numFish * foodPerDay

    foodLeft ← foodLeft - foodConsumed

    IF (foodLeft < 0) {

    daysStarving ← daysStarving + 1

    }

}

  • This simulation simplifies a real-world scenario into something that can be modeled in code and executed on a computer.
  • Summarize how the code works:

Examples

Card Flip 

import random

cards = ["Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King"] 
suits = ["Diamonds", "Hearts", "Spades", "Clubs"]

print(random.choice(cards) + " of " + random.choice(suits))

2 of Hearts

Coin Flip 

import random

def coinflip():         #def function 
    randomflip = random.randint(0, 1) #picks either 0 or 1 randomly 
    if randomflip == 0: #assigning 0 to be heads--> if 0 is chosen then it will print, "Heads"
        print("Heads")
    else:
        if randomflip == 1: #assigning 1 to be tails--> if 1 is chosen then it will print, "Tails"
            print("Tails")

#Tossing the coin 5 times:
t1 = coinflip()
t2 = coinflip()
t3 = coinflip()
t4 = coinflip()
t5 = coinflip()

Tails
Heads
Heads
Heads
Tails

Your turn: Change the code to make it simulate the flipping of a weighted coin.

Adding images (in Python)

  • Add a heads and tails images into your images directory with the correct names and run the code below
import random

# importing Image class from PIL package
from PIL import Image
 
# creating a object
im = Image.open(r"images/lebron.png")
image = Image.open(r"images/lebron1.png")

i=random.randint(0,1)

if i == 1:
    print("heads")
    display(im)

else:
    print("tails")
    display(image)

tails

In order to display an image in python, we can use the PIL package we previously learned about.

Spin the Wheel 

import random

print("Spin the wheel!")
print("----------------------------------")

n = 300
blue = 0
red = 0
 
for i in range(n):
    spin = random.randint(1,2)
    if spin == 1: # head
        blue = blue + 1
    else:         # tail
        red = red + 1
 
print('Number of blue:', blue)
print('Number of red:', red)

Your turn: Add a visual to the simulation!

Population Growth and Plots 

import random

totalPopulation = 50 
growthFactor = 1.00005
dayCount = 0 #Every 2 months the population is reported

while totalPopulation < 1000000:
    totalPopulation *= growthFactor
    #Every 56th day, population is reported
    dayCount += 1
    if dayCount == 56: 
        dayCount = 0
        print(totalPopulation)

Here we initialize the total population to be 50, then set the growth factor as 1.00005 (.005 percent change). It will print the population every 56th day until it reaches one million. It multiplies the current population by the growth factor in each iteration, and increments the day count. When the day count reaches 56, it prints the current population and resets the day count to 0.

Note! This simulation assumes that the growth factor remains constant as time progresses, which may not be a realistic assumption in real-world scenarios.

import matplotlib.pyplot as plt

# Define the initial population and growth rate
population = 100
growth_rate = 0.05

# Define the number of years to simulate
num_years = 50

# Create lists to store the population and year values
populations = [population]
years = [0]

# Simulate population growth for the specified number of years
for year in range(1, num_years+1):
    # Calculate the new population size
    new_population = population + (growth_rate * population)
    # Update the population and year lists
    populations.append(new_population)
    years.append(year)
    # Set the new population as the current population for the next iteration
    population = new_population
    
# Plot the population growth over time
plt.plot(years, populations)
plt.xlabel('Year')
plt.ylabel('Population')
plt.title('Population Growth Simulation')
plt.show()

If we create quantative data, we can plot it using the Matplotlib library.

Example on how simplification can cause bias 

import random

beak =  ["small-beak", "long-beak", "medium-beak"],
wing = ["small-wings", "large-wings", "medium-wings"],
height = ["short", "tall","medium"]


naturaldisaster = ["flood", "drought", "fire", "hurricane", "dustbowl"]


print("When a" , random.choice(naturaldisaster) , "hit",  random.choice(height), "birds died")

How does this simulation have bias? In general, bias can occur in simulations when certain assumptions or inputs are made that do not accurately reflect the real world, or when the simulation is designed to favor certain outcomes or perspectives.

JS examples

Dice Roll Binary Coin Flip Card Pull

Hacks

  • Answer all questions and prompts in the notes (0.2)
  • Create a simulation
    1. Create a simulation that uses iteration and some form of data collection (list, dictionary...) (0.4)
      • try creating quantative data and using the Matplotlib library to display said data
      • Comment and describe function of each parts
      • How does your simulation help solve/mimic a real world problem?
      • Is there any bias in your simulation? Meaning, are there any discrepancies between your program and the real event?
  • Answer these simulation questions (0.3)
  • Bonus: take a real world event and make a pseudocode representation or pseudocode on a flowchart of how you would make a simulation for it (up to +0.1 bonus)

Answered Questions

Question: A theme park wants to create a simulation to determine how long it should expect the wait time at its most popular ride. Which of the following characteristics for the virtual patrons would be most useful? Select two answers.

A. Ride preference—denotes whether a patron prefers roller coasters, other thrill rides, gentle rides, or no rides. B. Walking preference—denotes how far a patron is willing to walk in between rides. C. Food preference—denotes the type of food that a patron prefers to eat (e.g., chicken, burgers, salads). D. Ticket type—denotes whether the patron has a single-day pass, a multi-day pass, or an annual pass.

Answer: A and B.

Question: A programmer has created a program that models the growth of foxes and rabbits. Which of the following potential aspects of the simulation does NOT need to be implemented?

A. A representation of grass that rabbits must eat frequently to survive. B. Each rabbit may only have a certain amount of children per litter. C. Each fox must eat a rabbit frequently to survive. D. Each rabbit can only live to a certain age, assuming that they are not eaten.

Answer: A.

Question: The heavy use of chemicals called chlorofluorocarbons (CFCs) has caused damage to the Earth’s ozone layer, creating a noticeable hole over Antarctica. A scientist created a simulation of the hole in the layer using a computer, which models the growth of the hole over many years. Which of the following could be useful information that the simulation could produce?

A. The approximate length of time until the hole would be refilled (due to various atmospheric processes) B. The exact size of the hole at any given point in time C. The exact length of time until the hole would be refilled (due to various atmospheric processes) D. The exact depth of the hole at any point in time

Answer: A.

Question: Suppose that an environmentalist wanted to understand the spread of invasive species. What would be a benefit of doing this with a simulation, rather than in real life?

A. The species used in the simulation could be designed to mimic many different species at once. B. The species created could be quickly tested in multiple environments to better understand how its spread is affected by environmental factors. C. The simulation could be run much more quickly than in real life. D. All of the above.

Answer: D.

Question: A program is being created to simulate the growth of a brain-based on randomly determined environmental factors. The developer plans to add a feature that lets the user quickly run several hundred simulations with any number of factors kept constant. Why would this be useful? Select two answers.

A. It would allow the user to gather data without taxing the computer’s hardware. B. It would allow the user to see the effect of specific variables by ensuring that the others do not change. C. It would quickly provide the user with a large amount of data. D. It would make simulations more detailed.

Answer: B and C.

Question: Which of the following statements describes a limitation of using a computer simulation to model a real-world object or system?

A. Computer simulations can only be built after the real-world object or system has been created. B. Computer simulations only run on very powerful computers that are not available to the general public. C. Computer simulations usually make some simplifying assumptions about the real-world object or system being modeled. D. It is difficult to change input parameters or conditions when using computer simulations.

Answer: C.

REPEAT 24 TIMES {

    litersConsumed ← numPeople * litersPerHour

    litersLeft ← litersLeft - litersConsumed

    IF (litersLeft < 0) {

        break from loop;

    }
}

This simulation models the amount of water consumed and remaining after 24 hours based on the number of people and the average amount of water used per hour. This could be useful for estimating water needs for a household or for planning water usage for an event or gathering.