1. IST380 Loops got you going in circles? Nest them!
infinitely nested structure…
3/10 2day == 2d data
3/17 spring break!
3/24 no class
from finitely nested loops
3/ we meet again…
nested loops == 2d data
Schedule

2. What will Python think? User input meters = raw_input('How many m? ')
cm = meters * 100
print 'That is', cm, 'cm.'
You know you've become a programmer when you ask yourself…
What will Python think?
I think I like these units better than light years per year!

3. I think I like these units better than light years per year!
User input
meters = raw_input('How many m? ')
cm = meters * 100
print 'That is', cm, 'cm.'
What will Python think?
I think I like these units better than light years per year!

4. raw_input ALWAYS returns a string – no matter what has been typed!
User input
meters = raw_input('How many m? ')
cm = meters * 100
print 'That is', cm, 'cm.'
raw_input ALWAYS returns a string – no matter what has been typed!
What will Python think?
I think I like these units better than light years per year!

5. Fix #1: convert to the right type
meters_str = raw_input('How many m? ')
meters = float( meters_str )
cm = meters * 100
print 'That is', cm, 'cm.'
Electric: from
My tutorial is at:
Lasergene (a molecular biology suite of programs for aligning and comparing
DNA sequences, etc.)
Statview (statistical analysis)
KaleidaGraph (plotting & graphing)
Populus (programs that simulate ecological and evolutionary processes)
'42'
42.0
4200.0
name: meters_str type: string
name: meters type: float
name: cm
type: float

6. input interprets its input raw_input always returns a string
Fix #2: use input
meters = input('How many m? ')
cm = meters * 100
print 'That is', cm, 'cm.'
input interprets its input
raw_input always returns a string
I always use input -- but don't "quote" me on that.

7. hw6pr1: T. T. Securities (TTS)
Analyzes a sequence of stock prices
day
day 1
day 2
day 3
day 4
day 5
day 6
day 7
L = [ 40, 80, 10, 30, 27, 52, 5, 15 ]
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice:
The menu to implement:

8. Loop Review! hw6pr1: T. T. Securities (TTS)
Analyzes a sequence of stock prices
day
day 1
day 2
day 3
day 4
day 5
day 6
day 7
L = [ 40, 80, 10, 30, 27, 52, 5, 15 ]
Loop Review!
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice:
The menu to implement:

9. Calls a helper function Perhaps uc the reason for this?
A larger application
def menu():
""" prints our menu of options """
print "(1) Input a new list of numbers"
print "(2) I will divine the next element"
print "(9) Quit"
def main():
""" handles user input for our menu """
while True:
menu()
uc = input('Which option? ')
Calls a helper function
Perhaps uc the reason for this?

10. (9) Quit! (1) Get new list (2) other… def main():
""" handles user input for our menu """
L = [2,12,22,32] # a starting list
while True:
menu() # print menu
uc = input('Which option? ')
if uc == 9:
elif uc == 1:
elif uc == 2:
(9) Quit!
(1) Get new list
(2) other…

11. other functions, as needed
def main():
""" handles user input for our menu """
L = [2,12,22,32] # a starting list
while True:
menu() # print menu
uc = input('Which option? ')
if uc == 9:
elif uc == 1:
elif uc == 2:
break exits the loop
(9) Quit!
use input to get a new L
(1) Get new list
other functions, as needed
(2) other…

12. webbrowser.open_new_tab(url)
Functions you'll write
All use loops…
def average( L )
Menu
def stdev( L )
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice: 
(L[i] - Lav)2 i
len(L)
def minday( L )
def maxday( L )
webbrowser.open_new_tab(url)

13. Min price
Just call min ?
What's the idea for finding the smallest (minimum) price?
day
day 1
day 2
day 3
day 4
day 5
day 6
day 7
L = [ 40, 80, 10, 30, 27, 52, 5, 15 ]
m =
m is the "min so far"
track the value of the minimum so far as you loop over L

14. What about the day of the minimum price?
Min price vs. min day
day
day 1
day 2
day 3
day 4
day 5
day 6
day 7
L = [ 40, 80, 10, 30, 27, 52, 5, 15 ]
m = 40
m = 10
m = 5
5 is returned
def minprice( L ):
m = L[0]
for x in L:
if x < m:
m = x
return m
What about the day of the minimum price?

15. minday def minday( L ): m = L[0] mndy = 0
return the index of L's minimum.
>>> minday( [9, 8, 5, 7, 42] ) 2 1 2 3 4
index
def minday( L ):
m = L[0]
mndy = 0
for :
if < m:
m =
return mndy
How do we loop through the INDEX of each element?
How do we ensure m keeps track of the minimum?
How and where should we update mndy?
index-based loop

16. minday def minday( L ): m = L[0] mndy = 0 day = 0
return the index of L's minimum.
>>> minday( [9, 8, 5, 7, 42] ) 2 1 2 3 4
index
def minday( L ):
m = L[0]
mndy = 0
day = 0
for x in L:
if x < m:
m = x
mndy = day
day += 1
return mndy
Create a "counter" that will keep track of the current day.
IF we find a smaller min, save which day it was in mndy
Regardless, we add 1 to day so that we're keeping track!
element-based loop

17. personal motivation for TT securities…
LightPath, Summer 1999 ~ wedding gift…

18. LightPath, Summer 1999

19. LightPath, Spring 2000

20. Why it's called a brokerage
LightPath, Fall 2013

21. Investment analysis for the 21st century … and beyond!
T. T. Securities
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice:
Software side …
Hardware side…
Investment analysis for the 21st century … and beyond!

22. Investment analysis for the 21st century … and beyond!
T. T. Securities
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice:
Software side …
Hardware side…
Investment analysis for the 21st century … and beyond!

23. Investment analysis for the 21st century … and beyond!
T. T. Securities
(0) Input a new list
(1) Print the current list
(2) Find the average price
(3) Find the standard deviation
(4) Find the min and its day
(5) Find the max and its day
(6) Your TTS investment plan
(9) Quit
Enter your choice:
Back to the future
Software side …
Hardware side…
Investment analysis for the 21st century … and beyond!

24. What is the best TTS investment strategy here?
The TTS advantage!
Your stock's prices:
L = [ 40, 80, 10, 30, 27, 52, 5, 15 ]
What is the best TTS investment strategy here?
Day Price
To be realistic, however (for our VC backers and the SEC), you may only sell after you buy.

25. In CS, rules rule! L = [5,42,'hi'] s = 'hi'
Reference
Pointer id
L = [5,42,'hi']
s = 'hi'
'hi' 5 42
'hi' L s
L[0]
L[1]
L[2]
(1a) Numbers and strings are handled "by value"
(1b) Lists are handled "by reference"

26. The contents of the variable's "box" in memory are copied.
In CS, rules rule!
Reference
Pointer id
L = [5,42,'hi']
s = 'hi'
'hi' 5 42
'hi' L s
L[0]
L[1]
L[2]
(1a) Numbers and strings are handled "by value"
(1b) Lists are handled "by reference"
The contents of the variable's "box" in memory are copied.
(2) Inputs pass to functions "by value" 7
copy of fav 7
fav
f( fav )
fav

27. Python's two methods for handling data
Reference vs. Value
Python's two methods for handling data
L = [5,42,'hi']
s = 'hi'
Reference
Pointer id
Whee!
'hi' 5 42
'hi' s L
L[0]
L[1]
L[2]
Lists are handled by reference (the variables really hold a memory address)
Primitive data and strings are handled by value: imagine they hold the data

28. Python functions: pass by value
def conform(fav)
fav = 42
return fav
fav
def main()
print " Welcome! "
fav = 7
conform(fav)
print " My favorite # is", fav 7
fav
But what if the underlined part were absent… ?

29. Python functions: pass by value
def conform(fav)
fav = 42
return fav 42 7
fav
copy of fav
"pass by value" means the contents of fav are copied to fav
def main()
print " Welcome! "
fav = 7
conform(fav)
print " My favorite # is", fav 7
fav
But what if the underlined part were absent… ?

30. Python functions: pass by value
def conform(fav)
fav[0] = 42
fav[1] = 42
return fav
fav 7 11
def main()
print " Welcome! "
fav = [7,11]
conform(fav)
print " My favorite #s: ", fav
fav[0]
fav[1]
fav
But what if the underlined part were absent… ?

31. Python functions: pass by value
def conform(fav)
fav[0] = 42
fav[1] = 42
return fav
fav 7 11
def main()
print " Welcome! "
fav = [7,11]
conform(fav)
print " My favorite #s: ", fav
fav[0]
fav[1]
fav
But what if the underlined part were absent… ?

32. Lists are Mutable
You can change the contents of lists in functions that take those lists as input.
- Lists are MUTABLE objects
Those changes will be visible everywhere.
One rule rules them all: pass-by-value
Numbers, strings, etc. are IMMUTABLE – they can't be changed, only reassigned.

33. Differing approaches to rules …
Engineers
Physicists
different worldviews…
Mathematicians
CS?

34. Engineers believe equations approximate reality;
"the rules"
Engineers believe equations approximate reality;
Safety margins!
Grand Canyon Skywalk

35. Engineers believe equations approximate reality;
Physicists believe reality approximates equations…
Image forensics' verdict:
Fake!
Not a parabola, so not a real shot!

36. Banach-Tarski paradox
Engineers believe equations approximate reality;
Physicists believe reality approximates equations…
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"

37. Engineers believe equations approximate reality;
Physicists believe reality approximates equations…
Mathematicians don't care either way!
why settle for gears, when you could have fractal gears?
In CS?
Don't like reality? Build a new one!

38. arithmetic operations
Engineers believe equations approximate reality;
Physicists believe reality approximates equations…
Mathematics reasons about structural rules…
… and CS reasons about procedural ones.
for
lists
variables
while
Axioms
arithmetic operations
Definitions
if/else
proofs
programs
Insights, tools, truths
Insights, tools, algorithms
math worldview
CS worldview

39. One rule rules them all: everything's a list!
2D data!
One rule rules them all: everything's a list!

40. One rule rules them all: everything's a list!
Lists ~ 2D data
A = [ 42, 75, 70 ] 42 75 70
list
int
int
int A
One rule rules them all: everything's a list!
1D lists are familiar – but lists can hold ANY kind of data – including lists!

41. Lists ~ 2D data A = [ [1,2,3,4], [5,6], [7,8,9,10,11] ] 1 2 3 4 ? 5 6
Where's 3?
len(A[0])
len(A)
Replace 10 with 42.

42. Rectangular 2D data A = [ [1,2,3,4], [5,6,7,8], [9,0,1,2] ] 1 2 3 4 5
list
list
A[0] A
A[0][0] 5 6 7 8
list
A[1] 9 1 2
list
A[2]
A[2][3]
To try…
What is A[1][2]?
What does each component of A[1][2] mean ?
How many rows does A have, in general ?
How many columns does A have, in general ?

43. What are the resulting values in A?
Try it…
A = [ [1, 2, 3, 4],
[5, 6, 7, 8],
[9,10,11,12] ]
Starting with the 2d array A shown here, what are the values in A after running this code? A
Before
def mystery(A):
""" what happens to A ? """
NROWS = len(A)
NCOLS = len(A[0])
for row in range( 0,NROWS ):
for col in range( 0,NCOLS ):
if row == col:
A[row][col] = 42
else:
A[row][col] += 1
row 0
row 1
row 2
col 0
col 1
col 2
col 3 A
After
What are the resulting values in A?

44. hw6pr2: John Conway's Game of Life
red cells are "alive"
John Conway
Are there a few simple rules that could give rise to intricate, complex phenomena…
They need to be local
Chemistry ~ life! How?
white cells are empty

45. hw6pr2: John Conway's Game of Life
Grid World
Evolutionary rules
red cells are "alive"
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.
Only 3 rules
Any other # of neighbors and the central cell dies…
white cells are empty

46. Lab Problem: Conway's Game of Life
Grid World
Evolutionary rules
red cells are "alive"
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…
white cells are empty

47. Lab Problem: Conway's Game of Life
Grid World
Evolutionary rules
red cells are "alive"
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…
white cells are empty

48. Lab Problem: Conway's Game of Life
Grid World
Evolutionary rules
red cells are alive
Everything depends on a cell's eight neighbors
Exactly 3 neighbors give birth to a new, live cell.
What's next?
Exactly 2 or 3 neighbors keep an existing cell alive.
Any other # of neighbors and the central cell dies…
white cells are empty

49. next_life_generation( A )
Lab Problem: Creating life
next_life_generation( A )
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: the ? at left does NOT come to life! ?

50. next_life_generation( A )
Lab Problem: Creating life
next_life_generation( A )
old generation is the input, A
returns the next generation 1 2 3 4 5 1 2 3 4 5 1 1 2 2 3 3 4 4 5 5

51. Lab Problem: Creating life
Stable configurations:
"rocks"
Periodic
"plants"
period 2
period 3
Self-propagating
"animals"
glider

52. Lab Problem: Creating life
Many life configurations expand forever…
"Gosper glider gun"
"glider"
What is the largest amount of the life universe that can be filled with cells?
How sophisticated can Life-structures get?

53. extra! the Mandelbrot Set
z0 = 0
zn+1 = zn2 + c
Consider an update rule for all complex numbers c
Wait! What are complex numbers…?

54. Small values of c keep the sequence near the origin, 0+0j.
Complex numbers…
z0 = 0
zn+1 = zn2 + c
Consider an update rule for all complex numbers c
Small values of c keep the sequence near the origin, 0+0j. z3 c z1 z2 z4 z0
Real axis
Imaginary axis

55. Complex numbers are simply ordinary 2d points
x ~ "real" part
Complex numbers are simply ordinary 2d points
y ~ "imaginary" part
z = x + yi ~ complex #
z3 is 4 + 2i
z1 is ~ z3 z1 z2 z4 z0
Real axis
zlost
zlost is ~
Imaginary axis

56. Mandelbrot Definition
z0 = 0
zn+1 = zn2 + c
Consider an update rule for all complex numbers c
Which c's
stick around?
Small values of c keep the sequence near the origin, 0+0j.
Benoit B. Mandelbrot 1924 – 2010 c
Real axis c
Large values of c make the sequence head to infinity.
Imaginary axis

57. Python's complex #s >>> c = 3 + 4j >>> c.real 3.0
>>> c.imag
4.0
>>> abs(c)
5.0
Nothing's too complex for Python!

58. Mandelbrot Set ~ low-res version
The shaded area are points that do not diverge for z = z**2 + c

59. Higher-resolution M. Set
-2 + 1j
1 + 1j
connected
finite area
 perimeter!
-2 - 1j
1 - 1j
The black pixels are points that do not diverge for z = z**2 + c

60. Chaos! Zooming in reveals more and more detail, not less:
not 100% self-similar but quasi-self-similar

61. The black pixels are points that do not diverge for z = z**2 + c
What are these colors?

62. The black pixels are points that do not diverge for z = z**2 + c
escape velocities
What are these colors?

63. Happy Mandelbrotting!

64. Good luck with Hwks #5 and 6!
We meet again on March 31!