P3-M 4/25 Simulations
Creating simulations using pandas and python libraries
• Shruthi Malayath, Lina Awad, Lydia Cho, Sarah Liu, Jake Warren • 25 min read
- 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, 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:
print("Tails")
#Tossing the coin 5 times:
t1 = coinflip()
t2 = coinflip()
t3 = coinflip()
t4 = coinflip()
t5 = coinflip()
Tails Tails Heads Tails Tails
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
head = Image.open(r"images/head.jpeg")
tail = Image.open(r"images/tail.jpeg")
i=random.randint(0,1)
if i == 1:
print("heads")
display(head)
else:
print("tails")
display(tail)
tails
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
green = 0
for i in range(n):
spin = random.randint(1,3)
if spin == 1: # blue
blue = blue + 1
elif spin == 2: # green
green = green + 1
else: # red
red = red + 1
print('Number of red:', red)
print('Number of green:', green)
print('Number of blue:', blue)
Spin the wheel! ---------------------------------- Number of red: 104 Number of green: 98 Number of blue: 98
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)
50.14019267336515 50.28077842644361 50.421758361373264 50.5631335833823 50.704905200797775 50.847074325054315 50.98964207070282 51.13260955541927 51.27597790001347 51.41974822843774 51.563921667795874 51.70849934835185 51.85348240353876 51.99887196996765 52.14466918743647 52.290875198939005 52.43749115067384 52.5845181920533 52.731957475712534 52.87981015751845 53.028077396578915 53.17676035525173 53.325860199153716 53.47537809717 53.62531522146305 53.775672747481956 53.92645185397153 54.0776537229816 54.22927953987637 54.38133049334356 54.533807775403844 54.68671258142016 54.840046110106975 54.993809563539834 55.14800414716474 55.302631069807575 55.45769154368362 55.613186784406984 55.769118011000224 55.92548644590379 56.082293314985726 56.239539847551235 56.39722727635229 56.55535683759732 56.71392977096098 56.87294731959368 57.032410730131446 57.19232125270578 57.35268014095325 57.51348865202554 57.67474804659919 57.83645958888546 57.998624546640265 58.161244191174156 58.324319797362236 58.48785264365415 58.651844012084126 58.81629518828111 58.98120746147867 59.14658212452524 59.312420473894186 59.47872380969402 59.645493435678574 59.81273065925718 59.98043679150499 60.14861314717315 60.31726104469929 60.486381806217665 60.65597675756963 60.82604722831395 60.99659455173736 61.16762006486491 61.33912510847044 61.51111102708713 61.68357916901805 61.85653088634677 62.029967534947765 62.2038904744973 62.3783010684839 62.5532006842192 62.72859069284855 62.9044724693617 63.08084739260377 63.25771684528589 63.43508221399618 63.61294488921051 63.791306265303454 63.9701677405592 64.14953071718247 64.32939660130967 64.50976680301973 64.69064273634523 64.87202581928359 65.05391747380793 65.23631912587847 65.41923220545367 65.6026581465012 65.78659838700955 65.97105436899903 66.1560275385331 66.34151934572994 66.52753124477363 66.71406469392542 66.90112115553534 67.08870209605372 67.27680898604255 67.46544330018713 67.65460651730747 67.84430012037001 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808212.8600978188 810478.9705279225 812751.4347996128 815030.2707281307 817315.4961786682 819607.1290665091 821905.1873571683 824209.6890665338 826520.6522610073 828838.0950576467 831162.0356243073 833492.4921797828 835829.4829939516 838173.0263879179 840523.1407341555 842879.844456651 845243.1560310503 847613.0939848019 849989.6768973024 852372.9234000427 854762.8521767524 857159.4819635496 859562.8315490843 861972.9197746876 864389.7655345186 866813.3877757139 869243.8054985331 871681.0377565115 874125.103656607 876576.0223593509 879033.8130789979 881498.4950836754 883970.0876955378 886448.6102909151 888934.0823004647 891426.5232093263 893925.9525572724 896432.389938862 898945.8550035943 901466.3674560634 903993.9470561118 906528.613618986 909070.3870154906 911619.2871721458 914175.334071343 916738.5477515013 919308.9483072248 921886.5558894586 924471.390705649 927063.4730199015 929662.8231531383 932269.4614832586 934883.408445299 937504.6845315925 940133.3102919292 942769.306333718 945412.6933221479 948063.4919803509 950721.7230895628 953387.4074892879 956060.5660774591 958741.2198106066 961429.3897040186 964125.096831907 966828.3623275728 969539.2073835713 972257.6532518797 974983.721244062 977717.4327314354 980458.8091452414 983207.8719768105 985964.6427777322 988729.1431600227 991501.3947962954 994281.4194199304 997069.2388252458 999864.8748676664
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")
When a fire hit tall 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)