P3-M 4/25 Simulations
Creating simulations using pandas and python libraries
- Objectives
- What are simulations by College Board definition?
- Analyzing an Example: Air-Traffic Simulator
- Functions we often need (python)
- Functions we often need (js)
- College Board Question 1
- Examples
- Adding images (in Python)
- Population Growth and Plots
- Example on how simplification can cause bias
- JS examples
What are simulations by College Board definition?
- Simulations are _ that mimic more complex objects or phenomena from the real world
- Purposes include drawing inferences without the __ of the real world
- Simulations use varying sets of values to reflect the ___ state of a real phenomenon
- Often, when developing a simulation, it is necessary to remove specific __ or simplify aspects
- Simulations can often contain __ based on which details or real-world elements were included/excluded
- Simulations allow the formulation of ___ under consideration
- Variability and ___ 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
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.
// Math.random(); returns a random number
// Math.floor(Math.random() * 10); // Returns a random integer from 0 to 9:
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:
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))
import random
def coinflip(): #def function
randomflip = random.randint(0, 2) #picks either 0 or 1 randomly
if randomflip >= 1: #assigning 0 to be heads--> if 0 is chosen then it will print, "Heads"
print("Heads")
else:
if randomflip == 0: #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()
Your turn: Change the code to make it simulate the flipping of a weighted coin.
- 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/HeadsOn.jpg")
image = Image.open(r"images/TailsOn.jpg")
i=random.randint(0,1)
if i == 1:
print("heads")
display(im)
else:
print("tails")
display(image)
In order to display an image in python, we can use the PIL package we previously learned about.
import random
from PIL import Image
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)
if blue > red:
print("Blue wins!")
if red > blue:
print("Red wins!")
if red == blue:
print("Tie!")
Your turn: Add a visual to the simulation!
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.
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?
- Answer all questions and prompts in the notes (0.2)
- Create a simulation
- 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?
- Create a simulation that uses iteration and some form of data collection (list, dictionary...) (0.4)
- 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)
import random
# set up variables that represent games won by each team
suns = 0
nuggets = 0
# set up variable which represents amount of games played
games = 1
# while loop to simulate games until a team wins 4 games
while suns < 4 and nuggets < 4:
num = random.randint(1, 100)
# give suns 51% chance of winning each game
if num <= 51:
suns += 1
print(f"Game {games} winner: Suns")
# give nuggets 49% chance of winning each game
else:
nuggets += 1
print(f"Game {games} winner: Nuggets")
games += 1
# print the results of the simulated series
if suns > nuggets:
print(f"Suns defeat the Nuggets in {games - 1} games.")
if nuggets > suns:
print(f"Nuggets defeat the Suns in {games - 1} games.")
- The series mimics a playoff series between two NBA teams. It's mostly just for fun and doesn't really solve any problems one may face.
- There is a lot of potential bias in this simulation. There is a lot more going into a team winning a game than just straight odds such as injuries, home court advantage, crowd factor, fatigue, etc.
College Board Questions
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.
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.
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
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
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.
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 afer 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.