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.

 
 
 
 

Two east London boroughs are planning to tax nightlife to fund the clean up. Will it work?

A Shoreditch rave, 2013. Image: Getty.

No-one likes cleaning up after a party, but someone’s got to do it. On a city-wide scale, that job falls to the local authority. But that still leaves the question: who pays?

In east London, the number of bars and clubs has increased dramatically in recent years. The thriving club scene has come with benefits – but also a price tag for the morning clean-up and cost of policing. The boroughs of Hackney and Tower Hamlets are now looking to nightlife venues to cover these costs.

Back in 2012, councils were given powers to introduce ‘late night levies’: essentially a tax on all the licensed venues that open between midnight and 6am. The amount venues are expected to pay is based on the premises’ rateable value. Seventy per cent of any money raised goes to the police and the council keeps the rest.

Few councils took up the offer. Four years after the legislation was introduced, only eight local authorities had introduced a levy, including Southampton, Nottingham, and Cheltenham. Three of the levies were in the capital, including Camden and Islington. The most lucrative was in the City of London, where £420,000 was raised in the 2015-16 financial year.

Even in places where levies have been introduced, they haven’t always had the desired effect. Nottingham adopted a late night levy in November 2014. Last year, it emerged that the tax had raised £150,000 less than expected in its first year. Only a few months before, Cheltenham scrapped its levy after it similarly failed to meet expectations.


Last year, the House of Lords committee published its review of the 2003 Licensing Act. The committee found that “hardly any respondents believed that late night levies were currently working as they should be” – and councils reported that the obligation to pass revenues from the levy to the police had made the tax unappealing. Concluding its findings on the late night levy, the committee said: “We believe on balance that it has failed to achieve its objectives, and should be abolished.”

As might be expected of a nightlife tax, late night levies are also vociferously opposed by the hospitality industry. Commenting on the proposed levy in Tower Hamlets, Brigid Simmonds, chief executive at the British Beer and Pub Association, said: “A levy would represent a damaging new tax – it is the wrong approach. The focus should be on partnership working, with the police and local business, to address any issues in the night time economy.”

Nevertheless, boroughs in east London are pressing ahead with their plans. Tower Hamlets was recently forced to restart a consultation on its late night levy after a first attempt was the subject of a successful legal challenge by the Association of Licensed Multiple Retailers (ALMR). Kate Nicholls, chief executive at the ALMR, said:

“We will continue to oppose these measures wherever they are considered in any part of the UK and will urge local authorities’ to work with businesses, not against them, to find solutions to any issues they may have.”

Meanwhile, Hackney council intends to introduce a levy after a consultation which revealed 52 per cents of respondents were in favour of the plans. Announcing the consultation in February, licensing chair Emma Plouviez said:

“With ever-shrinking budgets, we need to find a way to ensure the our nightlife can continue to operate safely, so we’re considering looking to these businesses for a contribution towards making sure their customers can enjoy a safe night out and their neighbours and surrounding community doesn’t suffer.”

With budgets stretched, it’s inevitable that councils will seek to take advantage of any source of income they can. Nevertheless, earlier examples of the late night levy suggest this nightlife tax is unlikely to prove as lucrative as is hoped. Even if it does, should we expect nightlife venues to plug the gap left by public sector cuts?