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 abstractions that mimic more complex objects or phenomena from the real world
- Purposes include drawing inferences without the constraints of the real world
- Simulations use varying sets of values to reflect the changing state of a real phenomenon
- Often, when developing a simulation, it is necessary to remove specific details or simplify aspects
- Simulations can often contain bias based on which details or real-world elements were included/excluded
- Simulations allow the formulation of hypotheses under consideration
- Variability and randomness 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:
Starts with 4 fish and adding 20 fish per day and 160 is how much food is left and it is used to find how much time the fish can live without starving.
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, 1) #picks either 0 or 1 randomly
if randomflip == 2: #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()
Your turn: Change the code to make it simulate the flipping of a weighted coin.
Changing the number being checked to 2 leads to the coin being weighted.
- 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.png")
image = Image.open(r"images/TailsOn.png")
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
print("Spin the wheel!")
print("----------------------------------")
n = 300
blue = 0
red = 0
freq = ""
for i in range(n):
spin = random.randint(1,2)
if spin == 1: # head
blue = blue + 1
freq = freq + "🔵"
else: # tail
red = red + 1
freq = freq + "🔴"
print('Number of blue:', blue)
print('Number of red:', red)
print("Frequency: " + freq)
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?
This simulation shows bias because it doesn't take into account the beak and wing features of the bird. It just randomly selects a natural disaster and a height, without taking into account certain factors.
- 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)
Hacks
-
This simulation mimics the rolling of a fair die, both 100 and 1000000 times. This helps represent that a die is fair.
-
There is no bias in the program, this can be seen with the increase of iterations of the function, where all of the numbers show up at about the same number of times. In the real world, the surface on which the die is rolled or the way the die is made may cause some bias but in a perfect world there should be no bias.
Questions
- A, B
- A
- A
- D
- B, D
- C
import random # random selecton
import matplotlib.pyplot as plt # creation of graph
# this is the list in which each number is stored, 1 through 6 (this is why it's *6)
# initially, there is no frequency for each of the numbers, why it starts at 0
f = [0] *6
# recursion, rolling die multiple times
for i in range(100):
# rolling die to output random integer
roll = random.randint(1,6)
# adds to the frequency list, based on which number is rolled
f[roll-1] += 1
# x-axis of dataset
x = [1,2,3,4,5,6]
plt.bar(x, f) # defines axes, x and y
plt.title("Frequency of Rolls") # defines title
plt.xlabel("Number") # defines x-label
plt.ylabel("Frequency") # defines y-label
plt.show() # prints data
# import libraries needed for later use
import random # random selecton
import matplotlib.pyplot as plt # creation of graph
# this is the list in which each number is stored, 1 through 6 (this is why it's *6)
# initially, there is no frequency for each of the numbers, why it starts at 0
f = [0] *6
# recursion, rolling die multiple times
for i in range(1000000): # number is much greater
# rolling die to output random integer
roll = random.randint(1,6)
# adds to the frequency list, based on which number is rolled
f[roll-1] += 1
# x-axis of dataset
x = [1,2,3,4,5,6]
plt.bar(x, f) # defines axes, x and y
plt.title("Frequency of Rolls") # defines title
plt.xlabel("Number") # defines x-label
plt.ylabel("Frequency") # defines y-label
plt.show() # prints data
# in the end the output is about the same for all the numbers, showing no bias
