# How can you escape from a maze – and what does that teach us about city planning?

“Sorry, we live here now”. Image: Getty.

Mazes are in vogue at the moment, from HBO’s Westworld, to the return of the British cult gameshow, The Crystal Maze. But mazes have been around for millennia and one of the most famous mazes, the Labyrinth home of the Minotaur, plays a starring role in Greek mythology.

Which begs the question: what is the difference between a maze and a labyrinth? Although considered synonymous by some, it is generally accepted that a labyrinth contains only one path, often spiralling around and folding back on itself, in ever-decreasing loops, whereas a maze contains branching paths, presenting the explorer with choices and the potential for getting very, very lost.

While designing a maze can be a rewarding human task, computer scientists and mathematicians have a love of maze-generating algorithms. The algorithms tend to fall into two principal types: ones which start with a single, bounded space and then sub-divide it with walls (and doors) to produce ever smaller sub-spaces; and others which start with with a world full of disconnected rooms and then demolish walls to create paths/routes between them.

### The great escape

There are techniques for escaping from mazes, but first you need to be sure what kind of maze it is. Most methods work for “simple” mazes, that is, ones with no sneaky short-cuts via bridges or “passage loops” – circular paths that lead back to where they started.

So, assuming it is a simple maze, the method that many people know is “wall-following”. Essentially, you place one hand on a wall of the maze (it doesn’t matter which hand as long as you are consistent) and then keep walking, maintaining contact between your hand and the wall. Eventually, you will get out. This is because if you imagine picking up the wall of a maze and stretching its perimeter to remove any corners, you will eventually form something circle-like, part of which must form part of the maze’s outer boundary. This method of escape may not work, however, if the start or finish locations are in the maze’s centre.

But some mazes are deliberately designed to frustrate, such as the Escot Gardens’ beech hedge maze in Devon, which contains no fewer than five bridges, and so far from “simple”.

Another method of maze escape, known as Trémaux’s algorithm, works in all cases.

Imagine that, like Hansel and Gretel in the fairy story, you are able to leave a trail of “breadcrumbs” behind you as you navigate your way through the maze and then remember these rules: if you arrive at a junction you have not previously encountered (there will be no crumbs already on the trail ahead), then randomly select a way to go. If that leads you to a junction where one path is new to you but the other is not, then select the unexplored path. And if choosing between a once or twice-used path, choose the path used once, then leave a new, second trail behind you. The cardinal rule is never, ever select a path already containing two trails. This method is guaranteed, eventually, to get you out of any maze.

### Everyday mazes

So how is any of this maze stuff useful? Well, from the perspective of architecture and urban design, we want to avoid accidentally creating mazes. Mazes are fun, but are not necessarily something we want in our everyday lives – or in our way when we just want to get to work.

In the 1980s, the architectural theorist, Bill Hillier, observed that many of the most socially problematic housing estates were those that appeared to be somewhat “maze-like” in their layout. This begged the theoretical question: how do we actually measure the “maze-iness” of a place?

Barnsbury, in London: extremely unmaze-like. Image: Google Maps.

To answer this, Hillier developed the measure of “intelligibility”, which is the relationship between what is immediately visible from a single location in a maze/housing estate/neighbourhood and how accessible that same place is from other locations in the area. The measure ranges from 0 to 1: environments that score highly (greater than 0.5) tend to be quite intelligible, easy to understand and navigate, and frequently desirable – for example Barnsbury, in London.

Conversely, places with a low intelligibility score tend to be confusing, hard to navigate and, ultimately, maze-like – London’s Barbican Estate, although architecturally lauded, is so confusing that visitors need to follow the yellow lines in order to find their way around.

It was this measure of intelligibility that we used to design the game levels in the recent SeaHeroQuest game, a game designed to measure people’s navigational skills in order to further dementia research.

We “reverse-engineered” intelligibility in order to produce game levels that were more, or less, maze-like, to ensure a range of challenges for the players. So the mathematics of maze design is just as applicable in modern, dementia-battling apps as it was in distant Greek mythology.

Ruth Dalton is professor of building usability and visualisation, and Nick Dalton a lecturer in computing and communications, at Northumbria University, Newcastle.

# CityMetric is now City Monitor! Come see us at our new home

City Monitor is now live in beta at citymonitor.ai.

CityMetric is now City Monitor, a name that reflects both a ramping up of our ambitions as well as our membership in a network of like-minded publications from New Statesman Media Group. Our new site is now live in beta, so please visit us there going forward. Here’s what CityMetric readers should know about this exciting transition.

Regular CityMetric readers may have already noticed a few changes around here since the spring. CityMetric’s beloved founding editor, Jonn Elledge, has moved on to some new adventures, and a new team has formed to take the site into the future. It’s led by yours truly – I’m Sommer Mathis, the editor-in-chief of City Monitor. Hello!

My background includes having served as the founding editor of CityLab, editor-in-chief of Atlas Obscura, and editor-in-chief of DCist, a local news publication in the District of Columbia. I’ve been reporting on and writing about cities in one way or another for the past 15 years. To me, there is no more important story in the world right now than how cities are changing and adapting to an increasingly challenging global landscape. The majority of the world’s population lives in cities, and if we’re ever going to be able to tackle the most pressing issues currently facing our planet – the climate emergency, rising inequality, the Covid-19 pandemic ­­­– cities are going to have to lead the way.

That’s why City Monitor is now a global publication dedicated to the future of cities everywhere – not just in the UK (nor for that matter just in the US, where I live). Our mission is to help our readers, many of whom are in leadership positions around the globe, navigate how cities are changing and discover what’s next in the world of urban policy. We’ll do that through original reporting, expert opinion and most crucially, a data-driven approach that emphasises evidence and rigorous analysis. We want to arm local decision-makers and those they work in concert with – whether that’s elected officials, bureaucratic leaders, policy advocates, neighbourhood activists, academics and researchers, entrepreneurs, or plain-old engaged citizens – with real insights and potential answers to tough problems. Subjects we cover include transportation, infrastructure, housing, urban design, public safety, the environment, the economy, and much more.

The City Monitor team is made up of some of the most experienced urban policy journalists in the world. Our managing editor is Adam Sneed, also a CityLab alum where he served as a senior associate editor. Before that he was a technology reporter at Politico. Allison Arieff is City Monitor’s senior editor. She was previously editorial director of the urban planning and policy think tank SPUR, as well as a contributing columnist for The New York Times. Staff writer Jake Blumgart most recently covered development, housing and politics for WHYY, the local public radio station in Philadelphia. And our data reporter is Alexandra Kanik, whose previous roles include data reporting for Louisville Public Media in Kentucky and PublicSource in Pittsburgh, Pennsylvania.

Our team will continue to grow in the coming weeks, and we’ll also be collaborating closely with our editorial colleagues across New Statesman Media Group. In fact, we’re launching a whole network of new publications, covering topics such as the clean energy transition, foreign direct investment, technology, banks and more. Many of these sectors will frequently overlap with our cities coverage, and a key part of our plan is make the most of the expertise that all of these newsrooms combined will bring to bear on our journalism.

As for CityMetric, some of its archives have already been moved over to the new website, and the rest will follow not long after. If you’re looking for a favourite piece from CityMetric’s past, for a time you’ll still be able to find it here, but before long the whole archive will move over to City Monitor.

On behalf of the City Monitor team, I’m thrilled to invite you to come along for the ride at our new digs. You can follow City Monitor on LinkedIn and on Twitter. If you’re interested in learning more about the potential for a commercial partnership with City Monitor, please get in touch with our director of partnerships, Joe Maughan.

I want to thank and congratulate Jonn Elledge on a brilliant run. Everything we do from here on out will be building on the legacy of his work, and the community that he built here at CityMetric. Cheers, Jonn!

To our readers, on behalf of the City Monitor team, thank you from all of us for being such loyal CityMetric fans. We couldn’t have done any of this without you.

Sommer Mathis is editor-in-chief of City Monitor.