what's ahead? conway gives a whole new outlook on "loopy" ! john conway 10/18 no...

What's ahead?

Conway gives a whole new outlook on "loopy"

!

John Conway

10/18 no class - Fall break10/19 no new hw due

10/11 Dynamic & binary data10/12 ASCII art / C. cipher due

11/1 Objects and classes 211/2 Regular HW due

10/25 Dictionaries and objects 110/29 Images or life due

11/8 Final project ideas, p. 1

I'm a head!

ASCII diamond?

10-11-10 ?

Binary, briefly

8 bits = 1 byte = 1 box

The SAME bits can represent two different pieces of data,

depending on the type

type: str type: int00

1010

10

0010

1010

bits

bits

name: name:

value: value:

'*' 42

The same bits are in each container.But why these?

Base 10 What is 42 ?

424 tens + 2 ones

1231 hundred + 2 tens + 3 ones

ON

Es

colu

mn

TEN

s co

lum

nO

NEs

colu

mn

TEN

s co

lum

n

HU

ND

RED

s co

lum

n

--------

Base 2 Base 10

424 tens + 2 ones

101010

1231 hundred + 2 tens + 3 ones

ON

Es c

olu

mn

TEN

s co

lum

nO

NEs

colu

mn

TEN

s co

lum

n

HUN

DRED

s co

lum

n

each column represents

another power of the base

ON

Es c

olu

mn

TWO

s co

lum

n

FOURs

colu

mn

EIGH

Ts c

olu

mn

SIX

TEEN

s co

l.

THIR

TYTW

Os

col.

ON

Es c

olu

mn

TWO

s co

lum

n

FOURs

colu

mn

EIGH

Ts c

olu

mn

SIX

TEEN

s co

l.

THIR

TYTW

Os

col.

SIX

TYFO

URs

col

128s

colu

mn

Write 123 in binary…

10-11-10 ?

Conversions

from binary string to decimal number:

binstr = '101010'

N = int( binstr, 2 )

N is now 42.

Conversions

from binary string to decimal number:

from decimal number to binary string:

binstr = '101010'

N = int( binstr, 2 )

N is now 42.

def n2b( N ): if N<1: return '' return n2b(N/2) + str(N%2)

Use this helper function:

n2b( 42 )

'101010'

input any integer...

... and the binary string is returned

Hw5: binary, applied

Binary Image Encoding as raw bitsjust one big string of 64 characters

10101010 01010101 10101010 01010101 10101010 01010101 10101010 01010101

"1010101001010101101010100101010110101010010101011010101001010101"

Hw5: binary image compression

Binary Image

00000000 00000000 11111111 11111111 00000000 00000000 00000000 00001111

Encoding as raw bitsjust one big string of 64 characters

"0000000000000000111111111111111100000000000000000000000000001111"

If our images tend to have long streaks of unchanging data, how might we represent it more efficiently… (but still in binary)?

Hw5: binary image compression

Encoding as raw bits

One possible idea

0100001100000111001100

0 is the first digit

There are 16 of them.

1 is the next digit

Again, there are 16 of them.

just one big string of 64 characters

problems??

00000000 00000000 11111111 11111111 00000000 00000000 00000000 00001111

0 is the next digit

There are 28

1 is the final digit

There are 4

fixed-width image compression

a FIXED-width encoding is needed

00010000100100000001110010000100

0 is the first digit

There are 16 of them.

1 is the next digit

Again, there are 16 of them.

7 bits: # of repeats

1st bit holds 1 pixel value

7 bits holds the # of those values in a row

and so on…


8-bit data block 8-bit data block 8-bit data block 8-bit data block

original data original image

00000000 00000000 11111111 11111111 00000000 00000000 00000000 00001111

28 zeros 4 ones8 bits for each "block"

• If 7 bits holds the # of consecutive repetitions of data, what is the largest number of 1s or 0s that one block can represent?

• For hw5pr2, the standard images will be small (< 127 pixels)

B bits?00010000


8-bit data block

7 bits?

the pixel

hw5 pr2

def compress( I ): """ returns the RLE of the input binary image, I """

def uncompress( CI ): """ returns the binary image I from the run-length- encoded, "compressed" input, CI """

What function(s) might help here?

from cs5png import *binaryIm( I, ncols, nrows )

can download and run the image-file interface (not at all necessary)

for fun…

A start...

Write a function frontNum(s). It should return the # of times the first element of the input s appears consecutively AT THE FRONT of that string:

>>> frontNum('1111010')4

>>> frontNum('00111000010')2

Examples:

def frontNum(s):

What are the BEST and the WORST compression results you can get for an 8x8 input image (64 bits)?

How can you change fixed-length compression so that all compressed images are smaller than their originals ? That is,

how can we make compression always "work" ? EXTRA

Write a function frontNum(s). It should return the # of times the first element of the input s appears consecutively AT THE FRONT of that string:

def frontNum(s):

>>> frontNum('1111010')4

>>> frontNum('00111000010')2

Examples:

What are the BEST and the WORST compression results you can get for an 8x8 image input (64 bits)?

shortest compressed

representation

longest compressed representation

How can you change this compression algorithm so that all compressed images are smaller than their originals ? That is, how can we make compression

always work ?

EXTRA

Original Image T = 78/255 T = 120/255 Adaptive T

Binary images?

T = 120/255

Adaptive Threshold

Plot of total intensity across each row of pixels

What's in the image?

Why is it important to have binarized first?

What do these peaks

mean?

Which way is up?

This landscape image is determined to

contain a portrait document.

Intensity profiles

Which way is up?

Right-side up?

IS 313 Initial Project

Some preliminary thinking about project possibilities...

VPython

PyGame

Python for Android

Web Application ?• File upload ?

Python + SQL

• Image converter ?

• Library for 3d graphics

Connecting to external projects:

• Library for 2d game building

Python + ArcGIS

• Survey with stored results ?

• Other external devices • Databases? • Geog. displays

IS 313 Initial Project

This project has three deadlines:

• 10/25 Plan and initial reading/design

Using an external library? Make sure it's installed and an example works...

Start with the course's final project

• 11/8 Update with progress

• 11/15 Final version of this trial project

Make sure the plans and goals are reasonable, but potentially looking ahead...

There should be at least one piece of added, working functionality

Perhaps a revised plan for what to accomplish by 11/15

May choose to extend the initial project or completely change direction.

Potentially, a revised plan for what to accomplish by 11/15

Computing's Initial Project?

The Mark 1

Grace Hopper, Howard Aiken at Harvard

ran at 0.00001 MHz

5 tons, 530 miles of wiring765,299 distinct parts!

relay-based computer

Addition: 0.6 secondsMultiplication: 5.7 secondsDivision: 15.3 seconds

http://www-03.ibm.com/ibm/history/exhibits/markI/markI_reference.html

print: Making programs talk to you!

Debugging had to be discovered. I can remember the exact instant when I realized that a large part of my life from then on was going to be spent in

finding mistakes in my own programs.- Maurice Wilkes

Programming: the art of debugging an empty file.

- The Jargon Filehttp://www.tuxedo.org/~esr/jargon/

The first bug

Grace Hopper

“In the days they used oxen for heavy pulling, when one ox couldn't budge a log, they didn't try to grow a larger ox. We shouldn't be trying for bigger and better computers, but for

better systems of computers.”

from the UNIVAC 1

hw5pr3

Image processing...

import cs5png

Images are represented by Python lists...

IM = cs5png.getRGB( 'olin.png' )

newIM = invert( IM )

cs5png.saveRGB( IM )

hw5pr3

Creating a 4-pixel image from scratch....

PX = [ [ [255,0,0], [0,255,0] ]

cs5png.saveRGB( PX )

top row

1st column 2nd column

red, green, and blue components

Images... are just lists

How many dimensions do those lists have?

PX = [ [ [255,0,0], [0,255,0] ] [ [0,0,255], [255,255,0] ] ]

dimensions ~ complexity

Reference vs. Value

Changeable types: Unchangeable types:

liststring

int

float

bool

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

Reference,Pointer,

id

L = [7,11,'hi']

x7 11 'hi'

42

x = 42

“Pass By Value”

def main() """ calls conform """ print " Welcome to Conformity, Inc. "

fav = 7 conform(fav)

print " My favorite number is", fav

def conform(fav) """ sets input to 42 """ fav = 42 return fav

7

fav

fav

7

“Pass By Value”

def main() """ calls conform """ print " Welcome to Conformity, Inc. "

fav = 7 conform(fav)

print " My favorite number is", fav

def conform(fav) """ sets input to 42 """ fav = 42 return fav

7

fav

fav

PASSBY

VALUE

“Pass by value” means that data is copied when sent to a method

42

Passing lists by value…

def main() """ calls conform2 """ print " Welcome to Conformity, Inc. " fav = [ 7, 11 ] conform2(fav) print " My favorite numbers are", fav

def conform2(fav) """ sets all of fav to 42 """ fav[0] = 42 fav[1] = 42

What gets passed by value here?

favL[0] L[1]

7 11

fav

Passing lists by value…

def main() """ calls conform2 """ print " Welcome to Conformity, Inc. " fav = [ 7, 11 ] conform2(fav) print " My favorite numbers are", fav

def conform2(fav) """ sets all of fav to 42 """ fav[0] = 42 fav[1] = 42

favL[0] L[1]

7 11

fav

can change data elsewhere!

The reference is copied!

The conclusion

You can change the contents of lists in functions that take those lists as input.

Those changes will be visible everywhere.

(actually, lists or any mutable objects)

(immutable objects are safe, however)

Views of the world

Engineers think their equations approximate reality.

Views of the world

Engineers think their equations approximate reality. Physicists think reality approximates their equations.

Views of the world

Engineers think their equations approximate reality. Physicists think reality approximates their equations.

Mathematicians don't care.

Views of the world

Axioms

Definitions

Creating structure from a few simple facts...

Creating structure from a few simple actions ...

if/else

while

for

arithmetic operations

variablesarrays

Proof Algorithm

Engineers think their equations approximate reality. Physicists think reality approximates their equations. Mathematicians don't care.

computer science

Lists’ flexibility

Lists can hold ANY type of data

A = [ 42., 75., 70. ] 42.0 75.0 70.0float float floatlist

A

they don’t have to be horizontal

lists!

42.0

75.0

70.0

double

double

double

listAthey don’t have

to be horizontal lists!

Lists’ flexibility


A = [ 42., 75., 70. ] 42.0 75.0 70.0float float floatlist

A

Lsits’ flexibility


42.0 75.0 70.0double double doublelist

A

42 7 -11int int intlist

A

“go” “red” “sox!”

String String StringlistA

2d lists or arrays

Lists can hold ANY type of data -- including lists !

listA

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

listA

2d arrays

list

list

list

A[0]

A[1]

A[2]


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

listA

Jagged arrays

list

list

list

A[0]

A[1]

A[2]


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

Rows within 2d arrays need not be the same length…

listA

list

list

list

A[0]

A[1]

A[2]


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

Rows within 2d arrays need not be the same length…

We will not use jagged arraysat least in hw 10

Rectangular arrays

listA

list

list

list

A[0]

A[1]

A[2]

How many rows does A have, in general ?

How many columns does A have, in general ?

What does each piece of the syntax A[1][2] mean ?

A[1][2] = 42

A[2][3]

A[0][0]

Creating 1d and 2d lists...

def createRow( width ): """ does just that """ R = [] # start with nothing for col in range( width ): R = R + [0] return R

Creating 1d and 2d lists...

def createRow( width ): """ does just that """ R = [] # start with nothing for col in range( width ): R = R + [0] return R

def createBoard( height, width ): """ creates a 2d array! """ Bd = [] for row in range( ):

return Bd

Problem 4 -- “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 birthto a new, live cell!

• Exactly 2 or 3 neighbors keep anexisting cell alive

• Any other number of neighbors killthe central cell (or keep it dead)

John Conway

Problem 4 -- Life

Evolutionary rules

Grid World


red cells are alive





Problem 4 -- Life

Evolutionary rules

Grid World


red cells are alive





life out there...

Keep going!

Problem 4 -- Creating Life

0 1 2 3 4 50 1 2 3 4 5

0

1

2

3

4

5

0

1

2

3

4

5

newB = make_next_generation( oldB )

old generation or "board" new generation or "board"

Problem 4 -- Details

For each generation… • 0 represents an empty cell

• 1 represents a living cell

• outermost edge should always be left empty (even if there are 3 neighbors)

• compute all cells based on their previous neighbors before updating any of them

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

life out there...

Problem 2 -- to and beyond!

• Are there stable life configurations?

• Are there oscillating life configurations?

• Are there self-propagating life configurations?

"rocks"

"plants"

"animals"

period 3

period 2

Problem 2 -- to and beyond!

• Are there life configurations that expand forever?

• What is the largest amount of the life universe that can be filled with cells?

• How sophisticated can the structures in the life universe be?

Google for GOLLY, Game of Life

• Are all feasible configurations reachable?

Lab, Life!, and Homework…

import sys

for i in range(4): for j in range(8): sys.stdout.write('#') print

software object representing the screen's standard output

Without extra spaces…

Output

################################

method (function) that prints only its input

The not-so-subtle art of singling out the best (and worst) of anything…

Computing with language

Computing to the max You know this would make me hungry… if it weren't 7 pm!

Battle-tested ciphers - and how to break them !

Consider literature a bunch of strings ?

'm&ms'

[ 0, 42 ]

a comparison comparison

[ 4, 2 ]

True 'True'

'coffee'

> or <

Drawn Inward

Fall leaves when leaves fall.

Seasons by Mike Maguire

Beyond binary … to bits themselves

CS 101 Today

King of ANDs Queen of ORs

Jack of NOTs

Too many bits? Compress!

Olin during the day?

alien 2 diner 1

faces 2 diner 1

Hw #4 due Mon. 10/4

HW Notes

Lab binary & decimal

pr2 all your bases are belong to us!

pr3 image compression

Morning

Aft

mount 1 ghost 1

seven 0 ghost 0

extra image processing...

class's guesses

class's guesses

what's ahead? conway gives a whole new outlook on "loopy" ! john conway 10/18 no...

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