Today's lab begins with a quick tutorial on using Python, the built-in turtle and random libraries, and the on-line bioinformatics challenges, Rosalind. The main focus is on simulating Brownian motion by 1D and 2D random walks.
Software tools needed: Python IDLE programming environment and a web browser (for accessing lab and Rosalind).

Using Python

We will be using the IDLE programming environment for Python. The Python programming language and IDLE environment are freely available for many platforms from For this class, we are using Python 2, which is part of the Mac OSX operating system. Many features of the language (including the syntax of print statements) changed between the second and third version, and many popular packages are still only available for the second version.

To launch IDLE on your Macintosh:

  1. Open the Applications folder.
  2. Inside it, open the Utilities folder.
  3. Launch the Terminal application.
  4. The terminal will open a window where you can type commands. In that window, type:
    (remember to hit the enter/return key, so, the computer realizes you're done typing).
  5. Another window should open. Test to see if it is working by typing:
    print "Hello!"
    (remember to hit the enter/return key, so, the computer realizes you're done typing).

Once you have IDLE running, you can keep it in your dock by clicking on it and choosing options.

Turtle Library & for loops

For our first programs, we will use a built-in library (file of useful commands) for drawing using turtles. We will begin with a simple program and modify it to add functionality. This can be done from the Python prompt ( >>> in IDLE), but it is easier to store the program in a file and modify the file. To do this, go to the File menu of IDLE and choose New File (or type ⌘N).

In the new file window, type:

    import turtle

    teddy = turtle.Turtle()
    for i in range(4):
Indentation does matter, so, remember to indent the lines after the for, using TABs, so that they are included in the for-loop. Save the file as

Notes on saving files:

To run your program, go to the Run menu and choose Run Module. Python should open a new graphics window and draw a square.


What is this program doing? Let's go through, line-by-line:

Some Challenges

Modify your program to:
  1. Draw a hexagon.
  2. Draw an octagon.
  3. What does the following do? Work through it on paper, and then implement in Python to verify:
        import turtle
        teddy = turtle.Turtle()
        for i in range(40):
  4. Implement the following piece of pseudocode (i.e. directions that look very similar to code) as a complete program using turtle graphics:
        Repeat 45 times:
            Walk forward 100 steps
            Turn right 92 degrees

    Your output should look similar to:

  5. Draw a 5-pointed star.
  6. Print your name to the Python prompt 50 times.

Random Library

Another useful library is random library that generates (pseudo)-random numbers. The following:

	import random           #use the random library
	# other code here....
generates a random whole number between 0 and 6. Similarly, the command
generates a random whole number between 0 and 359. The command also allows random numbers to be chosen from multiples. For example: Let's write a program that turns a random amount each time. Here is an outline in comments (anything after the `#' is ignored by Python):
#Include the random and turtle libraries
#Create a turtle
#Have a loop that repeats 25 times
	#Inside that loop, 
	#Move forward 10 steps
	#Turn a random amount
#Close window on mouse click
Try to fill in each piece (if you're stuck, here is a possible solution).

Some Challenges

Modify your program to:
  1. Modify your random turning program to make random turns of 90 degrees only (i.e. 0, 90, 180, 270 degrees only).
  2. Modify your random turning program to make random turns of 180 degrees only (i.e. 0 and 180 degrees only).

Simulating Brownian Motion with Random Walks

We can use the programs above to simulate `random walks' where an object moves in a random direction (and a random distance forward). Random walks are well studied for modeling Brownian motion, diffusion models, paths of foraging animals, fluctuations in stock prices, and genetic drift.

For this lab, we will use the random turn programs to gather data to affirm or refute the hypothesis:

The longer the walk, on average, the farther east or west from the origin it ends.

Some notes:

Lab Write-Up

For each lab, you should submit a lab report by the target date to: kstjohn AT amnh DOT org. The reports should be about a page for the first labs and contain the following:

Target Date: 1 February 2016
Title: Lab 1: Simulating Brownian Motion with Random Walks
Name & Email:

Purpose: Give summary of what was done in this lab.
Procedure: Describe step-by-step what you did (include programs or program outlines).
Results: Show all data collected. Including screen shots is fine (can capture via the Grab program).
Discussion: Give a short explanation and interpretation of your results here.

Using Rosalind

This course will use the on-line Rosalind system for submitting programs electronically. The password for the course has been sent to your email. Before leaving lab today, complete the first challenge.