Code as a Liberal Art, Spring 2023

Unit 1, Tutorial 3 — Wednesday, February 15

Randomness; probability distributions; working with files

Today we're going to build on the reading discussion this week about the aleatory in computation by learning some techniques in computer program code for working with randomness. One of the things that we read and discussed was where the aleatory comes from within the rigid, formal strictures of digital machinery; how can randomness be generated from deterministic processes?

Today we will not be going into the technical details today around how to generate random and pseudo-random numbers. This topic involves complicated mathematics and we could spend an entire semester (or more!) just talking about those mathematic techniques. Instead, we will start with the fact that random numbers are in fact possible to generate, and we will learn the commands that Python provides to generate them.

Building on this, we will look at techniques for working with algorithms that incorporate randomness, or in other words, algorithms that are probabilistic: step-by-step procedures that incorporate and use values that are unpredictable, but within various ranges and likelihoods, which we can shape and control.

Some setup

For this lesson I'll be working with a few images. You can work with any images that you'd like as you work through these notes. But if you'd like to use the same images as me, you can download them here:

• air.jpg
• earth.jpg
• fire.jpg
• newspaper.png

Table of contents

The topics for today: (Click each to jump down to the corresponding section.)

1. Getting random: random.random()
2. Reproducible randomness: random.seed()
3. Probabilities
4. Probably distributions: More nuanced randomness shaping
5. Random choices
6. Random choices: files

I. Getting random: random.random()

In spite of all the discussion in your reading responses and in class about the complexity of generating random numbers, Python implements various random number generating algorithms and provides them to us as a collection of easy-to-use commands. These are provided by a library aptly called random.

To get started, simply import this library:

import random

Python documentation. So far, I have been sharing with you all the various commands and functions that you have been working with. But I want to point you to the Python documentation itself, so that you may explore by accessing it directly:

Official Python documentation at docs.python.org

This is the authoritative standard for all things Python. It is comprehensive and accurate, describing all aspects of the language. There are many other guides out there (w3schools.com is good, as is this guide called Automate the Boring Stuff with Python, by Al Sweigart) and these can be great. But if you want to go straight to the source for definitive information, the official Python docs cannot be beat.

Official programming language documentation like this can be hard to read. I often need to read slowly and carefuly, and think hard about the precise meanings of the terms that are used here. I usually have to read an explanation a few times before I completely wrap my head around all of its details and implications. But since this is the official documentation, that scrutiny is usually worth it for the thorough understanding that it can offer.

At your stage of learning to code, I know that it can be tempting simply to Google a problem: an error or a task you're trying to accomplish. But keep in mind that the results you will find will be unreliable or simply wrong. Even when the advice is correct, it may not be relevant — it may reference complicated techniques you have not learned yet, or it may be describing a problem subtly different from your own. In any case, reading and interpretting this advice is very difficult, and determining if it is correct and relevant is a very complicated task. Think of it like seeking medial advice from "Dr Google."

Thus, I would like to challenge you this semester to seek advice from reliable sources like the three above, and practice getting accustomed to how to navigate these resources for the information you seek.

In particular, I recommend you look at (a) the tutorial for an instructive introduction, and most powerfully, (b) the "Library Reference", which will tell you everything that you need to know (and more) about Python and its commands.

Let's experiment with using the official Python documentation today. Click on the "Library Reference", scroll about 1-2 screens down, and in the "Numeric and Mathematic Modules" section, find the entry labeled: "random — Generate pseudo-random numbers" (or, click here to go straight there). This section explains how to generate random numbers using Python.

To get started, let's look at the function called random(), which is essentially the heart of this module. To get acquainted, let's experiment with this in the Python shell:

>>> import random
>>> random.random()
0.5536582109886334
>>> random.random()
0.519728888240708
>>> random.random()
0.21552893690804353

As you can see, random() returns an unpredictable decimal number between 0 and 1.

There are numerous other shortcuts to make working with randomness easier. But let's start by spending some time with this one.

Using only this function, if you wanted a random integer (a number with no decimal places) between 0 and 9, what might you do? Have a look at this code and think about what it's doing:

>>> int( random.random() * 10 )

First of all, taking a decimal number between 0 and 1 and multiplying it by 10 is going to give us another number that is at minimum 0, and at maximum 10. Think about what you would get if you multiply 10 times .9999 (close to the largest value of random()). You'll get 9.999.

To summarize this: when you are starting with a number in the range of 0 to 1, multiplying scales a range. You are expanding that range of 0 to 1, into the range of 0 and whatever you multiply it by. random.random() * 100 is going to give us a random decimal number somewhere between 0 and 100. This is a useful principle to keep in mind.

But I said I wanted an integer (whole number). That is what the int() command does. It truncates (or cuts off) the decimal part of the number, returning a whole number from a decimal point. If you'd prefer, you could also use round(), which doesn't simply truncate, but actually rounds:

>>> int(.1)
0
>>> int(.6)
0
>>> round(.1)
0
>>> round(.6)
1

OK. Now, what if I wanted a number that was between 50 and 100? What is the range here? 50. So I could use my scaling technique like this: random.random() * 50. But that is going to give a number between 0 and 50, not between 50 and 100. What can I do here? I could simply add 50: 50 + random.random() * 50. Now I'm taking a random number scaled to the range of 0 to 50, and adding 50 to it, shifting that range to 50 to 100. To summarize this principle: when working with numbers like this, addition shifts a range.

Multiplying scales a range, and adding shifts the range. Using these techniques, you can shape the range of values we get from random.random() and manipulate them to span whatever range of randomness we wish. These are very useful principles for creative coding.

Fortunately, Python gives us some commands that we can use directly to achieve the same principles. (I think it is important and valuable later on to understand what is going on here, hence the above explanation before this reveal.)

If you want a randomly generated whole number (integer) from within some range, you can use: random.randrange(start,stop). (Python docs for this.) This takes two arguments and returns a random integer in between those arguments. So for example:

>>> random.randrange(5,10)
6
>>> random.randrange(5,10)
8
>>> random.randrange(5,10)
5

Note that this returns values that include the first arugment, but that are less than the second argument. In other words, random.randrange(5,10) will randomly return numbers from the list: 5, 6, 7, 8, and 9. In the language of mathematics (you may remember this from algebra or calculus) we say that the first argument is "inclusive" and the second is "exclusive", sometimes written as [5,10).

If you only pass in one argument, it returns a number between 0 and that argument:

>>> random.randrange(10)
8
>>> random.randrange(10)
3
>>> random.randrange(10)
1

Similar to with two arguments, when passing in one argument, the value is 0 is inclusive, and the argument is exclusive. So random.randrange(10) yields values in the range: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

II. Reproducible randomness: random.seed()

Another very useful idea in working with randomness is the idea of a random sequence of numbers that are reproducible. This can be useful for testing for example. Let's say you want to draw something that looks random, but you want it to look random the same way each time you run your code. You don't want it to be different each time. There is a command for this: random.seed()

When you call random.seed() with one numerical argument, every time you call random() after that, it will always return the same random-looking sequence. For example, if I run Python twice, I get two different random numbers each time:

$ python 
>>> import random
>>> random.random()
0.9998781067887237

$ python 
>>> import random
>>> random.random(1)
0.6638400757429336

But if I call random.seed(), I still get a random number, but it is the same each time:

$ python 
>>> import random
>>> random.seed(42)
>>> random.random()
0.7534071414623441

$ python 
>>> import random
>>> random.seed(42)
>>> random.random()
0.7534071414623441

This is called a pseudo-random number (it was discussed in the 10 PRINT book) because the numbers are drawn from a uniform distribution, so they appear random, but they are in fact deterministic.

This is very very useful in game development. For example, say you want to generate a character or a natural terrain, and you want its appearance to seem random. But you want that apperance to be the same each time the game is run, not changing every time. If that character has a name or ID number, you could use that as the seed. Each time you want to render that character, call seed() with their ID number, and the calls to random() that come after will seem random, but will be random in the same way each time.

You're probably familiar with this term because it is used in many games, such as Minecraft.

III. Probabilities

What if I want to generate some kind of digital object, say an image with randomly placed colored pixels on a white background, and I want to control how many colored pixels there are? You can ask if statements about random choices to control the probability.

For example, have a look at this code, which creates a new blank image, loops over all the pixels, and sets some of them to a color based on a random value:

Example 1

from PIL import Image
import random

# let's make a 100x100 white image

width = 100
height = 100

img = Image.new("RGB", (width,height), (255,255,255) )

for y in range(height):
    for x in range(width):

        r = random.random()

        if r > .5:
            img.putpixel( (x,y), (0,0,0) )

img.save("rando.png")

With this code, I'm using a nested loop again to iterate over each pixel in the image. The outter loop (y) repeats once for each row, and each time it repeats, the inner loop (x) repeats for each pixel in that row. For each pixel (i.e., for each x,y pair) this code picks a random number between 0 and 1 and if that number is greater than .5, it assigns that pixel to be black — otherwise the pixel will be white.

In other words, it loops over each pixel and assigns it to be black with 50% probability.

And what if I simply want there to be less black pixels in that image? Have a look at this:

Example 2

from PIL import Image
import random

# let's make a 100x100 white image

width = 100
height = 100

img = Image.new("RGB", (width,height), (255,255,255) )

for y in range(height):
    for x in range(width):

        r = random.random()

        if r > .9:
            img.putpixel( (x,y), (0,0,0) )

img.save("rando.png")

In Example 1, a pixel is drawn about 50% of the time: assuming a uniform distribution, a random number between 0 and 1 will be greater than .5 about half of the time. In Example 2 however, I am now only drawing the pixel if the random choice is greater than .9, so this will draw a pixel about 10% of the time. Notice the more sparse image.

IV. Probably distributions: More nuanced randomness shaping

The above two examples loop over every pixel in the image and decide with some probability whether that pixel should be black or not. What if we wanted to have a little more control over where and how those random pixels were placed?

Instead of looping over every pixel, we could loop some number of times, and each time we could pick random numbers to use as pixel coordinates.

Let's start by looping 500 times, each time randomly selected a pair of coordinates to use to place a black pixel:

Example 3

from PIL import Image
import random

# let's make a 100x100 white image

width = 100
height = 100

img = Image.new("RGB", (width,height), (255,255,255) )

# loop 500 times, and each time, pick a random x and a random y
# and draw a pixel there
for n in range(500):

    x = int( random.random() * 100 )
    y = int( random.random() * 100 )

    img.putpixel( (x,y), (0,0,0) )

img.save("rando.png")

But what if we didn't want the pixels evenly spaced out. What if we wanted them randomized, but clustered in some kind of way?

When we use random.random(), it is what's called a uniform distribution. Every single possible value is equally likely as the others. This creates an effect of total noise, like static on a broken TV.

If we want to create something that is random, but clustered in certain ways, we can use what's called a normal distribution, also known as a Gaussian distribution. You may have seen this depicted as a bell curve: values can still be chosen randomly within some range, but there is a greater likelihood that values will be chosen in the middle cluster than at the extremes. This type of probability distribution is used to model many things in the natural and social world, and we can use it for our purposes here.

Fortunately, Python provides a command for us to use here: random.gauss(). As the docs explain, this command takes two arguments. The first is the mean which corresponds to the middle point of the cluster, and the second corresponds to the standard deviation, which defines how tightly or widely flared out this distribution is.

Now instead of using random.random() and getting a completely uniform distribution, we can use a Gaussian distribution and shape the probabilities somewhat.

Example 4

from PIL import Image
import random

# let's make a 100x100 white image

width = 100
height = 100

img = Image.new("RGB", (width,height), (255,255,255) )

# loop 500 times, and each time, pick a random x and a random y
# and draw a pixel there
for n in range(500):

    x = int( random.gauss(50,10) )
    y = int( random.gauss(50,10) )

    img.putpixel( (x,y), (0,0,0) )

img.save("rando.png")

By changing the mean (the 50s in orange above) you could move the cluster around in the x or y dimension. And by changing the standard deviations (the 10s in orange above) you can change how tightly clustered the values are.

You can also mix and match these techniques. So for example here I'm using a Gaussian distribution for x (horizontal clustering), and a uniform distribution for y (evenly spaced out vertically).

Example 5

from PIL import Image
import random

# let's make a 100x100 white image

width = 100
height = 100

img = Image.new("RGB", (width,height), (255,255,255) )

# loop 500 times, and each time, pick a random x and a random y
# and draw a pixel there
for n in range(500):

    x = int( random.gauss(50,10) )
    y = int( random.random() * 100 )

    img.putpixel( (x,y), (0,0,0) )

img.save("rando.png")

I hope that you realize that you can use these exact techniques for more than just x,y values. You could use similar techniques for choosing random numbers to generate color patterns, letters, or any time you need a value in a creative coding context.

V. Random choices

What if I want to do something with randomness that is not just generating a number, but rather randomly selecting something from a list? I could do that like this:

>>> import random
>>> lyric = ['Birds', 'flying', 'high', 'you', 'know', 'how', 'I', 'feel']
>>> i = random.randrange( len(lyric) ) 
>>> lyric[i]
'know'
>>> i = random.randrange( len(lyric) )
>>> lyric[i]
'Birds'

What I'm doing here is creating a list called lyric, then remember that len(lyric) gives me the length of that list. So I'm passing the length of the list in to the command random.randrange(). That will always give me a value between 0 and the length of the list. I then use that value as the index to my list.

Turns out this is such a common operation that Python makes a shortcut for it: choice(). If you pass a list to this function, it will randomly select one item from the list:

>>> random.choice(lyric)
'know'
>>> random.choice(lyric)
'how'

Keep in mind that random.seed() also applies here. So if you ran the above command in a Python program, it would make different choices each time. But if you preceded it with random.seed() passing in a fixed number, it would make the same apparently random choices each time you ran the program.

VI. Random choices: files

Let's use this principle to randomly select a file from a folder of many files.

Let's say that I am in a directory (folder) called "Unit 1, Tutorial 4", and that it contains a subbolder called "images", like this:

From the command line, I can use ls to view the contents:

$ ls
images
$ ls images/
earth.jpg	fire.jpg	newspaper.png	smoke.jpg

Now I'm going to run Python and use a function called listdir(), which takes the name of a directory, and returns a list of all the files in that directory. This is in the os library, so I must import it first:

>>> from os import listdir
>>> listdir("images")
['newspaper.png', 'fire.jpg', 'earth.jpg', 'smoke.jpg']

Here I have passed in the name images, the name of my subfolder, and listdir() gives me an array of all files within that. Then I could choose a random file in that list like this:

>>> from os import listdir
>>> import random	
>>> files = listdir("images")
>>> random_file = random.choice(files)

Now I could go and use random_file as I would any filename — for example to open that file with Pillow.

Here is how you would do this in a Python program — and there is one more key step to the process:

from os import listdir, path
import random
from PIL import Image

files = listdir("images")
files.remove(".DS_Store")

random_file = random.choice(files)

img = Image.open( path.join("images",random_file) )

Note that I'm importing path, and then using path.join() in the last line. This is taking the directory name and the filename and joining them together into the path needed to access this file. If you tried to access the file without the directory name you'd get an error since the file is not in your current folder, but rather in a subfolder. (Remember the discussion about paths two weeks ago.)

This technique will be crucial in working on the homework for this week.

Warning. If you try the above technique, you may get an error message that looks something like this:

PIL.UnidentifiedImageError: cannot identify image file '.DS_Store'

If you see this error, it is because your directory contains a hidden file called .DS_Store. These are hidden files that Mac OS uses to store information about how your folder is displayed in Finder. Obviously it is not an image file, so PIL gives an error message when trying to open it. Wikipedia has some additioinal useful explanation of what these files are and what they contain.

Mac OS tries to hide these files from you, but you can see them if you type ls -a from the command line:

$ ls -a
.		.DS_Store	earth.jpg	newspaper.png
..		air.jpg		fire.jpg

(Note: this is from the command line, not the Python shell. Remember that you can always tell which shell you're in from the prompt. If you see >>>, then you are in Python. If you see $ or %, then you are in the command line. You can always enter the Python shell by typing python, and you can exit it by typing exit() or CONTROL-D.)

To verify the existence of .DS_Store from within a Python program or the Python shell, you could simply print the return value of listdir(), like this:

>>> from os import listdir
>>> files = listdir("images")
>>> files
['newspaper.png', 'air.jpg', '.DS_Store', 'fire.jpg', 'earth.jpg']

Fortunately, the solution for you is easy, simply remove them from your list of filenames:

>>> from os import listdir
>>> files = listdir("images")
>>> files
['newspaper.png', 'air.jpg', '.DS_Store', 'fire.jpg', 'earth.jpg']
>>> files.remove(".DS_Store")
>>> files
['newspaper.png', 'air.jpg', 'fire.jpg', 'earth.jpg']

That should prevent the PIL.UnidentifiedImageError.

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