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.


This fun map allows you to see what a nuclear detonation would do to any city on Earth

A 1971 nuclear test at Mururoa atoll. Image: Getty.

In 1984, the BBC broadcast Threads, a documentary-style drama in which a young Sheffield couple rush to get married because of an unplanned pregnancy, but never quite get round to it because half way through the film the Soviets drop a nuclear bomb on Sheffield. Jimmy, we assume, is killed in the blast (he just disappears, never to be seen again); Ruth survives, but dies of old age 10 years later, while still in her early 30s, leaving her daughter to find for herself in a post-apocalyptic wasteland.

It’s horrifying. It’s so horrifying I’ve never seen the whole thing, even though it’s an incredibly good film which is freely available online, because I once watched the 10 minutes from the middle of the film which show the bomb actually going off and it genuinely gave me nightmares for a month.

In my mind, I suppose, I’d always imagined that being nuked would be a reasonably clean way to go – a bright light, a rushing noise and then whatever happened next wasn’t your problem. Threads taught me that maybe I had a rose-tinted view of nuclear holocaust.

Anyway. In the event you’d like to check what a nuke would do to the real Sheffield, the helpful NukeMap website has the answer.

It shows that dropping a bomb of the same size as the one the US used on Hiroshima in 1945 – a relatively diddly 15kt – would probably kill around 76,500 people:

Those within the central yellow and red circles would be likely to die instantly, due to fireball or air pressure. In the green circle, the radiation would kill at least half the population over a period of hours, days or weeks. In the grey, the thing most likely to kill you would be the collapse of your house, thanks to the air blast, while those in the outer, orange circle would most likely to get away with third degree burns.

Other than that, it’d be quite a nice day.

“Little boy”, the bomb dropped on Hiroshima, was tiny, by the standards of the bombs out there in the world today, of course – but don’t worry, because NukeMap lets you try bigger bombs on for size, too.

The largest bomb in the US arsenal at present is the B-83 which, weighing in at 1.2Mt, is about 80 times the size of Little Boy. Detonate that, and the map has to zoom out, quite a lot.

That’s an estimated 303,000 dead, around a quarter of the population of South Yorkshire. Another 400,000 are injured.

The biggest bomb of all in this fictional arsenal is the USSRS’s 100Mt Tsar Bomba, which was designed but never tested. (The smaller 50MT variety was tested in 1951.) Here’s what that would do:

Around 1.5m dead; 4.7m injured. Bloody hell.

We don’t have to stick to Sheffield, of course. Here’s what the same bomb would do to London:

(Near universal fatalities in zones 1 & 2. Widespread death as far as St Albans and Sevenoaks. Third degree burns in Brighton and Milton Keynes. Over 5.9m dead; another 6m injured.)

Everyone in this orange circle is definitely dead.

Or New York:

(More than 8m dead; another 6.7m injured. Fatalities effectively universal in Lower Manhattan, Downtown Brooklyn, Williamsburg, and Hoboken.)

Or, since it’s the biggest city in the world, Tokyo:

(Nearly 14m dead. Another 14.5m injured. By way of comparison, the estimated death toll of the Hiroshima bombing was somewhere between 90,000 and 146,000.)

I’m going to stop there. But if you’re feeling morbid, you can drop a bomb of any size on any area of earth, just to see what happens.

And whatever you do though: do not watch Threads. Just trust me on this.

Jonn Elledge is the editor of CityMetric. He is on Twitter as @jonnelledge and also has a Facebook page now for some reason. 

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