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Random walks

A random walk involves moving in steps in an entirely random direction to a new location and repeating this process over and over.

Random walks have applications in engineering and many scientific fields including computer science, physics, chemistry and biology. Physicists use random walks to describe diffusion, the random spreading out of highly concentrated molecules in liquids and gases. Random walks are used in financial forecasting of stock prices. Social media uses random walks to suggest who you should follow. Random walks explain the observed behaviors of many processes in different fields, and serve as a fundamental model for the recorded random activity.

Create a random walk on a map

You will need:

  • A print out of a map with streets

  • A dice

  • A pen


  1. Select a starting point on your map and mark it with an X.

  2. Use the dice to decide which direction to walk.

  3. Draw an arrow up to the next street junction.

  4. Follow the rules below for each number.

  5. Keep going until you reach the edge of the map.

a. If you roll a 1, draw an arrow to the left

b. If you roll a 2, draw an arrow to the right

c. If you roll a 3, draw an arrow to the up

d. If you roll a 4, draw an arrow to the down

e. If you roll a 5, 6 or there is road for your number 1-4, roll again.

5. Keep going until you reach the edge of the map.

Well done! You have created a random walk.

Share your random walk on social media using #random

Create a random walk on fabric

You will need:

  • Fabric

  • A needle

  • Thread


  1. Look at the shape of your random walk on the map.

  2. Create the shape of your random walk on fabric.

  3. Thread the needle with the thread (Video: how to thread a needle)

  4. Thread the needle in and out of the fabric to create the shape of your walk.

  5. Have another go and create a different random walk.


How many arrows or stitches (or steps) are there in your random walks?

Why did your random walk end?

Can you make a second random walk on your map?

How do the random walks differ?

How many different random walks do you think are possible?


In this video you can see a self-avoiding walk with 100 million steps! It has been generated using a computational technique which uses an algorithm to roll the dice. Video credit: Nathan Clisby.

In this article and video called 'What was the chance of Ferris Bueller being caught on his day off?' from The Conversation you can read more about random walks. Article credit: Martin Archer. Video Credit: Martin Archer


Random Walks is a collaborative project by Lorna Dougan, Paul Beales, Christa Brown and Kalila Cook, and benefited from many enjoyable conversation with the Physics Craft Gathering group. Our interest in Random walks stems from our research on network formation of protein hydrogels. We use biomolecules called proteins as our 'thread' and create networks by connecting through sticky bits on their surface, through photo-activated chemical cross-linking. This creates networks of cross-linked proteins with a well defined shape and materials properties.

You can read more about our research here and in this Science highlight here

The project is supported by the Royal Academy of Engineering through their Ingenious Public Engagement awards which aim to engage the public with an exciting variety of engineering themes. With topics ranging from engineering solutions to the global climate emergency to engineering bedtime stories for young children, the projects will work with diverse audiences across the UK, igniting interest in the wonders of engineering to help inspire the next generation of engineers. The Ingenious programme offers grants to support creative public engagement with engineering projects while providing engineers with skills and opportunities to share their stories, passion and expertise with the public.

We acknowledge funding from the Engineering and Physical Sciences Research Council (EPSRC), Royal Academy Engineering (RAE) and Economic and Social Research Council (ESRC)

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