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
Algorithms
Emergence
Intelligence
Simulation
Information
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)
Imagine that the computer world consists of an
innite p
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 can have a red
occupant, a blue occupant, or else it is
e
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:
Beyondthe50minute(or75minute)
unit,towardshortercomposi'onalchunks
Pre
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 graphical notation for x+iy
Multiplying Two Complex Numb
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-zero sum
Two- vs. N-person games
Finite vs. innite n
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 Dilemma game.
Researchers can send in a program
to en
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
people are doing X
Public participation and anonymity
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
The major similarity to biological evolution:
differenti
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 genotype (which is
hidden) and phenotype (which is the ta
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 large number of parameters that
we could choose.
Examples
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 maybe there is no
way to tell if the question has really
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 maybe there is no
way to tell if the question has really
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 endless
checkerboard)
Now, ll one cell in the checkerboa
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,
with ever higher resolution
Now, count the number of b
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 description, but well be looking at
a few classes of basic
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,
character animation, galaxy formation,
spoken language, 3D
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 ip side of the pragmatic question (What makes
pas
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 physical combinations of computational and biological
mate
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, or #(blank)
Read/write head that can move one cell at a
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 numbers: (0, 1, 2, .)
Even numbers: (0, 2, 4, 6, )
Pr
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 procedure or function is
recursive if its denition invo
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 procedure or function is
recursive if its denition involves a
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]
IF n = 0
THEN RETURN 0
ELSE RETURN (n + Mystery1(n-1)
S
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 lettering.
This is the dog that chased the cat that caught
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 construct for
iteration:
repeat 12 [fd 25 rt 30]
Here was
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 (scaled) copies of
itself.
Squares, cubes, rectangles, tr
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
D = (log C)/(log S)
The logarithm here can be taken t
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:
Wednesday May 4, 1:30-4 PM
Easy ways for a problem to