4/1/15! 4/1/12! 4/1/07! IST 338 Rules ! z = z 2 + c John Conway HW - - PowerPoint PPT Presentation

4/1/15!

4/1/12!

4/1/07!

IST 338 Rules !

Three-in-a-row? Aliens rule at this…

John Conway

HW 9 (lab + 1 problem)

due Fri. 4/10

z = z 2 + c Rule #1: Don't follow this rule.

Simple rules can yield complex results!

Final projects: a look ahead…

In CS, rules rule!

(1b) Numbers and strings are handled "by value"

L

L[0] L[1] L[2] "Reference" "Pointer" id

L = [5,42,'hi']

5 42

'hi'

s

'hi'

s = 'hi' (1a) Lists are handled "by reference"

42,000,042

Reference vs. Value

Python's two methods for handling data

Lists are handled by reference: L really holds a memory address Numeric data and strings are handled by value: imagine they hold the data L

L[0] L[1] L[2] "Reference" "Pointer" id

L = [5,42,'hi']

5 42

'hi' 42,000,042

s

'hi'

s = 'hi'

x

7

x = 7

In CS, rules rule!

(1b) Numbers and strings are handled "by value" (2) Inputs pass to functions "by copy"

The contents of the variable's "box" in memory are copied.

7

fav

7

x

def f(x):

x is a copy of fav

L

L[0] L[1] L[2] "Reference" "Pointer" id

L = [5,42,'hi']

5 42

'hi'

s

'hi'

s = 'hi' (1a) Lists are handled "by reference"

42,000,042

in main: fav = 7 f(fav)

Python functions: pass by copy

def main() print " Welcome! " fav = 7 fav = conform(fav) print " My favorite # is", fav

7

fav fav def conform(fav) fav = 42 return fav

Python functions: pass by copy

def main() print " Welcome! " fav = 7 fav = conform(fav) print " My favorite # is", fav

7

fav def conform(fav) fav = 42 return fav

7 copy of fav "pass by copy" means the contents of fav are copied to fav

fav

But what if the underlined part were absent… ?

Rules rule!?

def conform1(fav) fav = 42 return fav def conform2(L) L = [42,42] return L

Try it!

Trace each f'n. What will main1, main2, and main3 print?

def conform3(L) L[0] = 42 L[1] = 42

fav fav L L 7

Notice that there are NO assignment statements after these function calls! The return values aren't being used…

L[0] 7

def main2() L = [7,11] conform2(L) print L def main1() fav = 7 conform1(fav) print fav def main3() L = [7,11] conform3(L) print L

L

L[1] 11

L

L[0] 7 L[1] 11

Lists are Mutable

You can change the contents of lists in functions that take those lists as input. Those changes will be visible everywhere.

• Lists are MUTABLE objects

Numbers, strings, etc. are IMMUTABLE – they can't be changed, only reassigned.

Differing approaches to rules …

Mathematicians CS? Engineers Physicists

Engineers believe equations approximate reality;

"the rules" Grand Canyon Skywalk

Safety margins!

Engineers believe equations approximate reality; Physicists believe reality approximates equations…

Not a parabola, so not a real shot!

http://www.youtube.com/watch?feature=player_embedded&v=WbaH52JI3So http://www.fourandsix.com/blog/2011/8/29/seriously-amazing-beer-pong-shots.html

Image forensics' verdict: Fake!

Mathematicians don't care either way! Engineers believe equations approximate reality; Physicists believe reality approximates equations…

A solid sphere can be split into 5 parts and rigidly reassembled into two spheres the same size as the original

Banach-Tarski paradox

Banach-Tarski XKCD the parts are "mist"

Mathematicians don't care either way! Engineers believe equations approximate reality; Physicists believe reality approximates equations…

why settle for gears, when you could have fractal gears?

Don't like reality? Build a new one! In CS?

Axioms Definitions

math worldview

Mathematics reasons about structural rules… Engineers believe equations approximate reality; Physicists believe reality approximates equations… … and CS reasons about procedural ones.

Insights, tools, mathematical truths

if/else while for arithmetic operations variables lists

CS worldview Insights, tools, algorithms

proofs programs Data Data

2D data!

Lists ~ 2D data

A = [ 42, 75, 70 ]

42 75 70

int int int list A

1D lists are familiar – but lists can hold ANY kind of data – including lists!

list A

Lists ~ 2D data

list list list A[0] A[1] A[2]

A = [ [1,2,3,4], [5,6], [7,8,9,10,11] ]

A[0][0] A[0][1] A[0][3] A[1][0] A[1][1] A[2][0] A[2][1] A[2][2] A[2][3] A[2][4]

len(A[0]) len(A) Replace 10 with 42.

1 2 4 ? 3 5 6 7 8

10

9

11

Where's 3?

list A list list list A[0] A[1] A[2]

Using len, how many rows does A have, in general ? Using len, how many columns does A have, in general ? What does each component of A[1][2] mean ? What is A[1][2]?

A[2][3] A[0][0]

A = [ [1,2,3,4], [5,6,7,8], [9,0,1,2] ]

1 2 3 4 5 6 7 8 9 1 2

To try…

Rectangular 2D data

Try it…

def mystery(A): """ what happens to A ? """ NROWS = len(A) NCOLS = len(A[0]) for r in range( 0,NROWS ): for c in range( 0,NCOLS ): if A[r][c] == 4: A[r][c] = 1 else: A[r][c] += 1 After – with the code as written…

A

Write in the resulting values in A:

A = [ [4, 2, 2, 2], [2, 2, 4, 4], [2, 4, 4, 2] ]

Starting with the 2d array A shown above, write the values in A after running the code?

4 2 2 2 2 2 4 4 2 4 4 2

Before

A

row 0 row 1 row 2 col 0 col 1 col 2 col 3

hw9pr2

4 2 2 2 2 2 4 4 2 4 4 2 def inarow_2east(A): """ what happens to A ? """ NROWS = len(A) NCOLS = len(A[0]) for r in range( 0,NROWS ): for c in range( 0,NCOLS ):

Before

A

row 0 row 1 row 2 col 0 col 1 col 2 col 3

A = [ [4, 2, 2, 2], [2, 2, 4, 4], [2, 4, 4, 2] ]

How would you change the code above to produce a True where the original value is equal to its neighbor to the right?!

(False, if no neighbor or a different neighbor.)

F T T F T F T F F T F F

Challenge:

First, try it by eye…

A = [ [' ','X','O',' ','O'], ['X','X','X','O','O'], [' ','X','O','X','O'], ['X','O','O',' ','X'] ]

inarow_3east('X', 1, 0, A)

checker start row start col LoL

col 0 col 1 col 2 col 3 col 4 row 0 row 1 row 2 row 3

… then, on hw9pr2, by Python!

First, try it by eye…

A = [ [' ','X','O',' ','O'], ['X','X','X','O','O'], [' ','X','O','X','O'], ['X','O','O',' ','X'] ]

inarow_3east('X', 1, 0, A) inarow_3south('O', 0, 4, A) inarow_3southeast('X', 2, 3, A) inarow_3northeast('X', 3, 1, A)

checker start row start col LoL

True

col 0 col 1 col 2 col 3 col 4 row 0 row 1 row 2 row 3

… then, on hw9pr2, by Python!

John Conway

hw9pr1 (lab): Conway's Game of Life

1970

60˚ 70˚ 20˚ 10˚ ? (no trig)

Geometer @ Princeton

Solution: www.cs.yale.edu/homes/toyama/tri/sol.html

simple rules ~ surprising behavior 1995

Lab Problem: Conway's Game of Life

Evolutionary rules Grid World

• Everything depends on a

cell's eight neighbors red cells are "alive" white cells are empty

• Exactly 3 neighbors give

birth to a new, live cell.

• Exactly 2 or 3 neighbors

keep an existing cell alive.

• Any other # of neighbors

and the central cell dies…

white cells are empty

Lab Problem: Conway's Game of Life

Evolutionary rules Grid World

• Everything depends on a

cell's eight neighbors red cells are "alive"

• Exactly 3 neighbors give

birth to a new, live cell.

• Exactly 2 or 3 neighbors

keep an existing cell alive.

• Any other # of neighbors

and the central cell dies…

white cells are empty

Lab Problem: Conway's Game of Life

Evolutionary rules Grid World

• Everything depends on a

cell's eight neighbors red cells are "alive"

• Exactly 3 neighbors give

birth to a new, live cell.

• Exactly 2 or 3 neighbors

keep an existing cell alive.

• Any other # of neighbors

and the central cell dies…

red cells are alive white cells are empty

Lab Problem: Conway's Game of Life

Evolutionary rules Grid World

• Everything depends on a

cell's eight neighbors

• Exactly 3 neighbors give

birth to a new, live cell.

• Exactly 2 or 3 neighbors

keep an existing cell alive.

• Any other # of neighbors

and the central cell dies…

For each cell…

• 3 live neighbors – life!
• 2 live neighbors – same
• 0, 1, 4, 5, 6, 7, or 8 live

neighbors – death

• computed all at once, not cell-

by-cell, so the ? at left does NOT come to life!

http://www.math.com/students/wonders/life/life.html

?

Lab Problem: Creating life

next_life_generation( A )

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

next_life_generation( A )

• ld generation is the input, A

returns the next generation

Lab Problem: Creating life

?

Stable configurations: Periodic

"rocks" "plants" "animals" period 3 period 2

Lab Problem: Creating life

Self-propagating

glider

Many life configurations expand forever… What is the largest amount of the life universe that can be filled with cells? How sophisticated can Life-structures get?

www.ibiblio.org/lifepatterns/

"glider" "Gosper glider gun"

Lab Problem: Creating life

Ex Cr: the Mandelbrot Set

Consider an update rule for all complex numbers c

z0 = 0 zn+1 = zn

2 + c

Nothing's too complex for Python!

Python's complex #s

>>> c = 3 + 4j >>> c.real 3.0 >>> c.imag 4.0 >>> abs(c) 5.0

c z0 z1 z2 z3 z4 Real axis Imaginary axis

Mandelbrot Definition

Consider an update rule for all complex numbers c

z0 = 0 zn+1 = zn

2 + c

Small values of c keep the sequence near the

• rigin, 0+0j.

z5

some "stick around":

• scillate or converge

Mandelbrot Definition

Real axis Imaginary axis

Other values of c make the sequence head to infinity.

Benoit B. Mandelbrot 1924 – 2010

c

Small values of c keep the sequence near the

• rigin, 0+0j.

c

Consider an update rule for all complex numbers c

z0 = 0 zn+1 = zn

2 + c

hw9pr3: the Mandelbrot Set

Consider an update rule for all complex numbers c

z0 = 0 zn+1 = zn

2 + c

hw9pr3: the Mandelbrot Set

Consider an update rule for all complex numbers c

z0 = 0 zn+1 = zn

2 + c

hw9pr3 Mandelbrot Set ~ points that stick around

The shaded area are points that do not diverge for z = z**2 + c

Higher-resolution M. Set

The black pixels are points that do not diverge for z = z**2 + c

• 2 + 1j
• 2 - 1j

1 + 1j 1 - 1j

connected finite area ∞ ∞ ∞ ∞ perimeter!

Complex things always consisted of simple parts…

Chaos?

Chaos!

http://www.youtube.com/watch?v=0jGaio87u3A not self-similar but quasi-self-similar

This was a "naturally occurring" object where zooming uncovers more detail, not less:

Before the M. Set, complex things were made of simple parts:

The black pixels are points that do not diverge for z = z**2 + c

What are these colors?

What are these colors?

The black pixels are points that do not diverge for z = z**2 + c

escape velocities

Atlas of the M. Set

In the Seahorse Valley….

Happy Mandelbrotting!

www.cs.hmc.edu/~jgrasel/projects

http://www.youtube.com/watch?v=0jGaio87u3A

Today is about the our final projects + it's a sales pitch for the three possible options:

Tis the season for final projects…

vPool TextID Picobot

Final projects

Final CS assignment

• pen-ended

comprehensive

Working solo or in a pair is OK

same projects for black/gold Pairs need to work together - in the same place - and they need to share the work equally... three choices…

Project options…

TextID Picobot! VPool

See the IST 338 Final Projects page…

Pre-planned possibilities

TextID Picobot! VPool

at least to think about…

Big ideas: (1) Implement Picobot in Python (2) Train Python to write successful Picobot programs!

The Picobot project

talk about going full circle...

Picobot returns!

Picobot's classes

class Program:

0 xxxx -> N 0 0 Nxxx -> W 0 0 NxWx -> S 0 0 xxWx -> S 0 0 xxWS -> E 0 0 xxxS -> E 0 0 xExS -> N 0 0 xExx -> N 0 0 NExx -> S 1 1 xxxx -> S 1 1 Nxxx -> E 1 1 NxWx -> E 1 1 xxWx -> N 1 1 xxWS -> N 1 1 xxxS -> W 1 1 xExS -> W 1 1 xExx -> S 1 1 NExx -> W 0

What in Python could most usefully hold all of these rules? What type should self.rules be? self.rules[ (1,"NExx") ] = ("W",0)

key value

Picobot's classes

class World:

What in Python could most usefully hold the environment? What type should self.room be?

+++++++++++++++++++++++++ +oooooPooooooooooooooooo+ +o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +ooooooooooooooooooooooo+ +++++++++++++++++++++++++

+

• P

Picobot: Visited: Wall:

Picobot's classes

class World:

What in Python could most usefully hold the environment? What type should self.room be?

+++++++++++++++++++++++++ +oooooPooooooooooooooooo+ +o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o

• +

+o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +o o+ +ooooooooooooooooooooooo+ +++++++++++++++++++++++++

+

• P

Picobot: Visited: Wall:

Current State: 1 Current Rule: 1 N*W* -> X 2

++++++++++ +o++o+o+++ +oooooo ++ ++++o++ + +oooo+++++ ++++o + +oooo+++ + ++++o+++++ +Pooo + ++++++++++

The Picobot project

First build an ASCII simulation

Picobot started here… and is now here…

Program evolution

program p1 program p2

An example of genetic algorithms, used for

• ptimizing hard-to-describe functions.

Start with a population of, say, ~200 random Picobot programs…

Program evolution

program p1 fitness = 0.03 program p2 fitness = 0.05

An example of genetic algorithms, used for

• ptimizing hard-to-describe functions.

Then, evaluate the fitness

• f all of those programs

Evaluate? How??

program p1 fitness = 0.03 program p2 fitness = 0.05

mate + mutate the fittest rulesets

to create a new generation

• f ~200 programs…

program c1 fitness = 0.19

fitness = 0.90

Repeat this "survival of the fittest" process for many generations…

… and by the end, your Python code should have evolved a much more capable Picobot program!

Project options...

TextID Picobot! VPool

the TextID project

First paragraph of The Cuckoo's Calling by R. Galbraith

kottke.org/13/08/how-jk-rowling-was-found-to-be-robert-galbraith

the TextID project

Big ideas: (1) Build lexical models of bodies of text… (2) Create a similarity score that defines Rowlingness Shakepearity

NYTimes-iness WSJournalicity vs. vs. your own choice of two comparisons… Big Bang Theory? Arrested Development vs.

TextID model

class TextModel

word-frequencies stem-frequencies

word-length-freq.'s /

all will be Python dictionaries…

WS: { "love": 50, "spell": 8, … } JKR: { "love": 11, "spell": 277, … } WS: { "lov": 612, "spell": 9, … } JKR: { "lov": 98, "spell": 306, … } WS: { 4: 7042, 5: 6203, … } JKR: { 4: 980, 5: 42005, … } sentence-length-freq.'s

Processing steps: one idea

Split the text into words… Clean the words … Remove all non-alphabetic characters Find sentence lengths using punctuation Create dictionaries of the words and their lengths Stem the words Create a dictionary of word stems You're ready to match against another model!

This looks familiar...

Stemming

Or tries to output the root!

stem( "party" ) "parti" stem( "parties" ) "parti" stem( "love" ) "lov" stem( "loving" ) "lov" An algorithm that outputs the root of the input word. these don't have to be words, just stems…

Stemming

Or tries to output the root!

stem( "party" ) "parti" stem( "parties" ) "parti" stem( "love" ) "lov" stem( "loving" ) "lov" An algorithm that outputs the root of the input word. these don't have to be words, just stems…

Model matching

Suppose we have two dictionaries: WS: { "love": 50, "spell": 8, "thou": 42 } JKR: { "love": 25, "spell": 275, "potter": 700 }

"potter" is not here. "thou" is not here.

How could we give a match score for this New dictionary against each one above? New: { "love": 3, "thou": 1, "potter": 2, "spam": 4 }

Naïve Bayes classification

WS: { "love": 50, "spell": 8, "thou": 42 } JKR: { "love": 25, "spell": 275, "potter": 700 }

"potter" is not here. "thou" is not here.

New: { "love": 3, "thou": 1, "potter": 2, "spam": 4 }

score vs. WS score vs. JKR

50 100 50 100 50 100 42 100 100 25 1000 25 1000 25 1000 1000 700 1000

score = 0 score = 0

Naïve Bayes classification

WS: { "love": 50, "spell": 8, "thou": 42 } JKR: { "love": 25, "spell": 275, "potter": 700 }

"potter" is not here. "thou" is not here.

New: { "love": 3, "thou": 1, "potter": 2, "spam": 4 }

score vs. WS score vs. JKR

50 100 50 100 50 100 42 100 1 100 25 1000 25 1000 25 1000 1 1000 700 1000

score = 0.0525 score = 0.000011

Naïve Bayes classification

Naïve Bayes classification

Project options...

TextID Picobot! VPool

3d graphics-based game using VPython

vPool

Let's play! I'll take your cue...

A few constraints

• physically interacting "pool balls"
• allow the user to direct 1+ objects
• needs a game goal + be winnable!

not really very constrained at all!

• must detect some collisions and

model their results on the motion

The vPool project

Funky Physics is OK… !

Collisions with walls should be handled... Collisions with other pool balls should be handled... You need pockets – or some other game objective A few examples to get you thinking…

VPython was designed to make 3d physics simulations simpler to program

So far, VPython has eventually worked for everyone...

Project options…

TextID Picobot! VPool

Project details…

Enjoy the projects!

• … we certainly do!