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.The Conversation

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

This article was originally published on The Conversation. Read the original article.

 
 
 
 

How bad is the air pollution on the average subway network?

The New York Subway. Image: Getty.

Four more major Indian cities will soon have their own metro lines, the country’s government has announced. On the other side of the Himalayas, Shanghai is building its 14th subway line, set to open in 2020, adding 38.5 km and 32 stations to the world’s largest subway network. And New Yorkers can finally enjoy their Second Avenue Subway line after waiting for almost 100 years for it to arrive.

In Europe alone, commuters in more than 60 cities use rail subways. Internationally, more than 120m people commute by them every day. We count around 4.8m riders per day in London, 5.3m in Paris, 6.8m in Tokyo, 9.7m in Moscow and 10m in Beijing.

Subways are vital for commuting in crowded cities, something that will become more and more important over time – according to a United Nations 2014 report, half of the world’s population is now urban. They can also play a part in reducing outdoor air pollution in large metropolises by helping to reduce motor-vehicle use.

Large amounts of breathable particles (particulate matter, or PM) and nitrogen dioxide (NO2), produced in part by industrial emissions and road traffic, are responsible for shortening the lifespans of city dwellers. Public transportation systems such as subways have thus seemed like a solution to reduce air pollution in the urban environment.

But what is the air like that we breathe underground, on the rail platforms and inside trains?

Mixed air quality

Over the last decade, several pioneering studies have monitored subway air quality across a range of cities in Europe, Asia and the Americas. The database is incomplete, but is growing and is already valuable.

Subway, Tokyo, 2016. Image: Mildiou/Flickr/creative commons.

For example, comparing air quality on subway, bus, tram and walking journeys from the same origin to the same destination in Barcelona, revealed that subway air had higher levels of air pollution than in trams or walking in the street, but slightly lower than those in buses. Similar lower values for subway environments compared to other public transport modes have been demonstrated by studies in Hong Kong, Mexico City, Istanbul and Santiago de Chile.

Of wheels and brakes

Such differences have been attributed to different wheel materials and braking mechanisms, as well as to variations in ventilation and air conditioning systems, but may also relate to differences in measurement campaign protocols and choice of sampling sites.

Second Avenue Subway in the making, New York, 2013. Image: MTA Capital Construction/Rehema Trimiew/Wikimedia Commons.

Key factors influencing subway air pollution will include station depth, date of construction, type of ventilation (natural/air conditioning), types of brakes (electromagnetic or conventional brake pads) and wheels (rubber or steel) used on the trains, train frequency and more recently the presence or absence of platform screen-door systems.

In particular, much subway particulate matter is sourced from moving train parts such as wheels and brake pads, as well as from the steel rails and power-supply materials, making the particles dominantly iron-containing.


To date, there is no clear epidemiological indication of abnormal health effects on underground workers and commuters. New York subway workers have been exposed to such air without significant observed impacts on their health, and no increased risk of lung cancer was found among subway train drivers in the Stockholm subway system.

But a note of caution is struck by the observations of scholars who found that employees working on the platforms of Stockholm underground, where PM concentrations were greatest, tended to have higher levels of risk markers for cardiovascular disease than ticket sellers and train drivers.

The dominantly ferrous particles are mixed with particles from a range of other sources, including rock ballast from the track, biological aerosols (such as bacteria and viruses), and air from the outdoors, and driven through the tunnel system on turbulent air currents generated by the trains themselves and ventilation systems.

Comparing platforms

The most extensive measurement programme on subway platforms to date has been carried out in the Barcelona subway system, where 30 stations with differing designs were studied under the frame of IMPROVE LIFE project with additional support from the AXA Research Fund.

It reveals substantial variations in particle-matter concentrations. The stations with just a single tunnel with one rail track separated from the platform by glass barrier systems showed on average half the concentration of such particles in comparison with conventional stations, which have no barrier between the platform and tracks. The use of air-conditioning has been shown to produce lower particle-matter concentrations inside carriages.

In trains where it is possible to open the windows, such as in Athens, concentrations can be shown generally to increase inside the train when passing through tunnels and more specifically when the train enters the tunnel at high speed.

According to their construction material, you may breath different kind of particles on various platforms worldwide. Image: London Tube/Wikimedia Commons.

Monitoring stations

Although there are no existing legal controls on air quality in the subway environment, research should be moving towards realistic methods of mitigating particle pollution. Our experience in the Barcelona subway system, with its considerable range of different station designs and operating ventilation systems, is that each platform has its own specific atmospheric micro environment.

To design solutions, one will need to take into account local conditions of each station. Only then can researchers assess the influences of pollution generated from moving train parts.

The ConversationSuch research is still growing and will increase as subway operating companies are now more aware about how cleaner air leads directly to better health for city commuters.

Fulvio Amato is a tenured scientist at the Spanish National Research CouncilTeresa Moreno is a tenured scientist at the Institute of Environmental Assessment and Water Research (IDAEA), Spanish Scientific Research Council CSIC.

This article was originally published on The Conversation. Read the original article.