Class 23: Simulation

Held: Tuesday, 3 October 2006

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.
• Lab: Simulation.
• Reading: Simulation.

Due

• HW8.

Assignments

• HW9.

Notes:

• There were some difficulties on HW8. We may spend a bit of time discussing it.
• Tuesday extra at 1 p.m.: Installing Linux.

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?