lec92 15 ist338 - hmc computer sciencedodds/ist338/slides/lec92_15_ist338.pdf · reference vs....

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"

LL[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

LL[0] L[1] L[2]


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

fav7

x

def f(x):

x is a copy of fav

LL[0] L[1] L[2]


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!


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!



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!



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…



… 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 intlist

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 8 109 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 0 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…

AWrite 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

BeforeArow 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 ):

BeforeArow 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 rulesGrid 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…






red cells are "alive"







red cells are alive












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 )

0 1 2 3 4 50 1 2 3 4 5

0

1

2

3

4

5

0

1

2

3

4

5

next_life_generation( A )

old generation is the input, A returns the next generation


?

Stable configurations:

Periodic

"rocks"

"plants"

"animals"

period 3

period 2


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"


Ex Cr: the Mandelbrot Set

Consider an update rule

for all complex numbers c

z0 = 0

zn+1 = zn2 + 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

z1z2

z3

z4

Real axis

Imaginary axis

Mandelbrot Definition



z0 = 0

zn+1 = zn2 + c

Small values of c keep

the sequence near the

origin, 0+0j.

z5

some "stick around":

oscillate or converge

Mandelbrot Definition

Real axis

Imaginary axis

Other values of c

make the sequence

head to infinity.

Benoit B.

Mandelbrot

1924 – 2010c

Small values of c keep

the sequence near the

origin, 0+0j.

c



z0 = 0

zn+1 = zn2 + c

hw9pr3: the Mandelbrot Set



z0 = 0

zn+1 = zn2 + 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:


What are these colors?

What are these colors?


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

PicobotI've got my eyes on some of these

projects!Eye'll bet !

Final projects

Final CS assignment

open-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…

Eye, eye!

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

+o

PPicobot:

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

optimizing 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

optimizing hard-to-describe functions.

Then, evaluate the fitness

of 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

of ~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

Though Robin Ellacott’s twenty-five years of life had seen their

moments of drama and incident, she had never before woken up in the certain knowledge that she

would remember the coming day for as long as she lived.

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 Developmentvs.

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…

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,


score vs. WS score vs. JKR

50

100

50

100

50

100

42

100

0

100

25

1000

25

1000

25

1000

0

1000

700

1000

score = 0 score = 0


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,


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

Project options...

TextID

Picobot!

VPool

3d graphics-based

game using VPythonvPool

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!

An unusual variation on VPool

… we certainly do!

lec92 15 ist338 - hmc computer sciencedodds/ist338/slides/lec92_15_ist338.pdf · reference vs....

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