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 programs that mimic more complex objects or phenomena from the real world
- Purposes include drawing inferences without the consequences of the real world
- Simulations use varying sets of values to reflect the hypothetical state of a real phenomenon
- Often, when developing a simulation, it is necessary to remove specific problems or simplify aspects
- Simulations can often contain bias based on which details or real-world elements were included/excluded
- Simulations allow the formulation of predictions 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:
There are 4 fish who eat 20 food per day with 160 food left in total. The simulation runs for 5 days. and sees if the fish starve or run out of food.
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 == 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()
Your turn: Change the code to make it simulate the flipping of a weighted coin.
import random
def coinflip(): #def function
randomflip = random.randint(0, 2) #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:
print("Tails")
#Tossing the coin 5 times:
t1 = coinflip()
t2 = coinflip()
t3 = coinflip()
t4 = coinflip()
t5 = coinflip()
- 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/coinHeads.png")
image = Image.open(r"images/coinTails.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
from PIL import Image
blueSquare = Image.open(r"images/bluesquare.png")
redSquare = Image.open(r"images/redsquare.png")
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:
display(blueSquare)
elif red > blue:
display(redSquare)
else:
display(blueSquare)
display(redSquare)
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?
It's completely random. There's no correlation between the properties of the birds and the natural disaster.
- 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
- Create a simulation that uses iteration and some form of data collection (list, dictionary...) (0.4)
# Plant growth simulation
import matplotlib.pyplot as plt
# Variables for the simulation
growth_rate = 1.4
initial_height = 2
days_to_simulate = 14
# Empty list to store the plant's height over time
heights = [initial_height]
# Simulate the growth of the plant over time
for day in range(1, days_to_simulate + 1):
# Calculate plant's height on this day
new_height = heights[day - 1] * growth_rate
# Add the new height to the list of heights
heights.append(new_height)
# Plot the plant's growth over time
plt.plot(range(days_to_simulate + 1), heights)
plt.title("Plant Growth Over Time")
plt.xlabel("Days")
plt.ylabel("Height (in.)")
plt.show()
- How does your simulation help solve/mimic a real world problem?
This simulation can help us understand how plants grow and develop over time, and can be used to study the effects of different growth rates, environmental conditions, and other factors on plant growth.
- Is there any bias in your simulation? Meaning, are there any discrepancies between your program and the real event?
One potential bias in this simulation is that it assumes a constant growth rate over time, which may not be the case in real life.
-
Answer these simulation questions (0.3)
- A & B
- A
- A
- D
- B & C
- C
-
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)
One real world event that could be simulated is the spread of a contagious disease among a population. See below
import random
import pandas as pd
population_size = 500
initial_infected = 10
transmission_rate = 0.8
recovery_rate = 0.1
simulation_days = 14
susceptible = [True] * population_size
infected = [False] * population_size
recovered = [False] * population_size
for i in range(initial_infected):
infected[i] = True
susceptible[i] = False
results = pd.DataFrame(columns=['Day', 'Susceptible', 'Infected', 'Recovered'])
for day in range(simulation_days):
for i in range(population_size):
if infected[i]:
for j in range(population_size):
if susceptible[j]:
if random.random() < transmission_rate:
infected[j] = True
susceptible[j] = False
if random.random() < recovery_rate:
infected[i] = False
recovered[i] = True
elif not recovered[i]:
susceptible[i] = True
current_state = {'Day': day+1,
'Susceptible': sum(susceptible),
'Infected': sum(infected),
'Recovered': sum(recovered)}
results = pd.concat([results, pd.DataFrame(current_state, index=[0])], ignore_index=True)
results['Day'] = results['Day'].astype(int)
results.set_index('Day', inplace=True, drop=True)
print(results)