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 abstractions that mimic more complex objects or phenomena from the real world
    • Purposes include drawing inferences without the contraints 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...

Simulation vs. Experiment

  • Experiment definition: procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact

So, why use a simulation?

  • Advantages:
    • Can be safer
    • More cost-effective
    • More efficient
    • More data in less time
  • Disadvantages:
    • Not as accurate as experiments
    • outside factors not included (ex: in rolling dice simulation gravity and air resistance)
  • When do you not use a simulation?
    • when a situation already has set results/data (won't change)
    • examples: a score in a game, most purchased food, average yearly wage

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 

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.

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.
  • Explain what each part of the code does