Class 25: Simulation

Held: Monday, 3 March 2003

Summary: Today we consider how to make Scheme simulate potentially unpredictable events, like the rolling of dice or the flipping of coins.

Related Pages:

• EBoard.
• Reading on Simulation.
• Lab.

Notes:

• How many of you are planning to miss the class on Friday, 14 March?
• I've graded homework 2. You should have received your grade in the mail. I've also written some notes on the assignment.
• Are there questions on homework 3?
• I see that some of you answer questions that read compute the following by writing a procedure. You don't always need to write procedures.
• I've received an interesting email about students using images in their CS151 projects. So ... don't use other people's images.
• I've graded exam 1. We'll spend a few minutes going over key issues.

Overview:

• The Problem of Simulation.
• Scheme's random procedure.
• Simulating the roll of dice.
• Lab.

Simulation

• At times, we write programs to model real-world situations:
  • The effect of pollutants on a lake
  • The waiting time in line at Wal-Mart
  • The playing of a card or dice game
• Each of these situations has some aspect of unpredicatability (even if we ignore the butterfly flappings of chaos theory)
• Can we write such programs in Scheme?

Random

• Scheme provides a simple procedure, random, to provide some fodder for simulations and any other times that you want to play with unpredictable behavior.
• (random n) produces an "unpredictible" number in the range [0 .. n-1].
• That's all you need to know right now.

Dice

• Here's a simple simulation problem: Simulate the roll of a single six-sided die.
  • Yes, die is the singular of dice
• Here's one possibility

  (+ 1 (random 6))
  

• See the reading for an alternative.

Lab

• Do the lab.
• Reflect?