The Computational World
Mike Eisenberg
MWF 2-2:50
ECCR 155
http:/l3d.cs.colorado.edu/~ctg/classes/compworld11/Home.html
Computer Science
GEOMETRY
Some Major Topics of this
Course
Computability
Algor
Cellular Automata and the Game
of Life (continued)
Problem Set 2 Due Friday
Reading assignment for Monday 2/28:
http:/www.wired.com/wired/archive/12.10/tail.html
Cellular Automaton (Vanilla
Version)
Neighborhoods and Earthquakes
Problem Set 2 Due Friday
Reading assignment for Monday 2/28:
http:/www.wired.com/wired/archive/12.10/tail.html
Schellings Model of
Neighborhoods
Each cell in the grid ca
The Social Impact of Computing:
Lets Start with This Classroom
Problem Set 2 due TODAY
Reading assignment for Monday 2/28:
http:/www.wired.com/wired/archive/12.10/tail.html
Predic'on1:
Beyondthe50minu
Returning to Fractals:
Julia Sets
Complex Numbers a
Whirlwind Introduction
The idea of i as square root of -1
Adding and subtracting complex numbers
Multiplying and dividing complex numbers
A gr
Game Theory, Continued: From
Zero-Sum to Non-Zero-Sum
Problem Set 3 due on FRIDAY!
Blue
Cooperate
Cooperate
Defect
3
3
0
5
5
0
1
1
Red
Defect
Game Theory: Basic Taxonomy
Zero- vs. non
Game Theory:
The Prisoner s Dilemma
Tournament, and Beyond
Axelrod s idea: hold a computer
tournament in which each
contestant is a program that will
play a series of rounds of the
Prisoner s Di
Big Games
Problem Set 4 has been sent out:
due Friday April 8 in class
Games in the Large
Games where I wish to do X only if few
people are doing X
Games where I wish to do X only if lots of
p
Articial Life
Problem Set 4 due on Friday (4/8)
Synthetic Psychology (or
maybe synthetic biology ):
building minds and animals
Dawkins Blind Watchmaker
A model of an evolution-like system
T
Articial Life, continued
Problem Set 4 due on Friday (4/8)
Dawkins Blind Watchmaker
A model of an evolution-like system
The major similarity to biological evolution:
differentiation between ge
Genes and Swarms
Problem Set 4 due today
Guest lectures Monday and
Wednesday of next week!
Genetic Algorithms: the General
Idea
Suppose we wish to explore a design space in
which there are a larg
The Biggest Open Question in
Computer Science
Final Exam:
Wednesday May 4, 1:30-4 PM
Different ways a problem can be
hard
It could be ill-dened, or vague, or maybe
there isn t a solution, or ma
The Biggest Open Question in
Computer Science
Final Exam:
Wednesday May 4, 1:30-4 PM
Different ways a problem can be
hard
It could be ill-dened, or vague, or maybe
there isn t a solution, or ma
More on DLAs; Cellular
Automata and the Game of Life
Problem Set 2 due in class
Friday, Feb. 25
Diffusion-Limited Aggregation
Imagine that the entire plane is divided up
into square cells (like an en
Fractals, Continued
Problem Set 2 due
Friday, February 25
Hard copy in class
Box-Counting Dimension
Make a grid over the set that you are interested: 10
by 10, 100 by 100, 1000 by 1000, and so forth,
A Recipe for Making Fractals
Problem Set 2 due in two weeks
(2/25)
A Math Interlude: Maps
A map is a function from points in the plane (x, y) to
points in the plane (x, y)
Thats a pretty general des
Turings Ideas, part I: the Test
http:/l3d.cs.colorado.edu/~ctg/classes/compworld11/Home.html
What I cannot create, I do not
understand
Richard Feynman
Bird ocks, earthquake patterns, game design,
cha
Turings Ideas, part II: the Test
and the Machine
http:/l3d.cs.colorado.edu/~ctg/classes/compworld11/Home.html
Some Questions to Consider
The pragmatic question (What makes passing this test so
hard?)
The Turing Machine
and the Limits of Computers
http:/l3d.cs.colorado.edu/~ctg/classes/
compworld11/Home.html
Searles Chinese Room
An alternative way of thinking about computational thought:
direct phy
Some Innities Are Bigger
than Others
http:/l3d.cs.colorado.edu/~ctg/classes/
compworld11/Home.html
The Turing Machine: or, What is
a computer?
Innite tape of individual cells, each containing
a 1, 0,
A Mysterious Limitation on
Computers; Followed By Things
All Computers Do Well
http:/l3d.cs.colorado.edu/~ctg/classes/
compworld11/Home.html
Countable Innite Sets
Natural numbers: (1, 2, 3, )
Whole
From Iteration to Recursion
Note: Problem Set 1 has been sent out via
email. It will be due in class (hard copy
only, please) on Monday, Feb. 7
RECURSION:
the basic denition
In a computer program, a
Recursion (continued)
Note: Problem Set 1 has been sent out via
email. It will be due in class (hard copy
only, please) on Monday, Feb. 7
RECURSION:
the basic denition
In a computer program, a proced
Recursive Procedures,
Recursive Language
Note: Problem Set 1 has been sent out via
email. It will be due in class (hard copy
only, please) on Monday, Feb. 7
Some Practice Examples
Dene Mystery1 [n]
I
From Language to Iteration
Reminder: Problem Set 1 is due
Monday 2/7 in class (hard copy).
Looking at
Recursion in Language
I bought a shovel from the store with the door
with the sign with red lett
Math Experiments through
Iteration
Reminder: Problem Set 1 is due
Monday 2/7 in class (hard copy).
And now, a fresh look at iteration
Iteration: to do something repeatedly
We have already seen a co
Self-Similarity; Rethinking the
Idea of Dimension
Problem Set 1 due today;
Problem Set 2 to be posted this week
Self-Similarity
A shape is self-similar if it is composed of
more than one smaller (sca
Fractals: Starting Out
Problem Set 2 has been sent out:
Due Friday Feb. 25 (hard copy)
Look at the two numbers that weve identied for
self-similar shapes: C copies, 1/S scaling.
Dene a new quantity
The Biggest Open Question in
Computer Science (part 3)
FRIDAY CLASS MEETS 2 PM IN
DLC 170 (go in front door of DLC, up staircase)
Problem Set 5 due in class on
Friday, April 29
Final Exam:
We