The Dictionary of Human Geography

defined as those in extreme incomepoverty
and/or living in the so-calledfaminebelt of
sub-Saharan Africa. Many suffer fromhuman
rightsabuses (see the website for the non-
governmental organization ATD Fourth
World: http://www.atd-fourthworld.org)..) Other
Fourth World peoples suffer from pervasive
social exclusionon grounds ofethnicity,
genderor religion. Many Fourth World
peoples reject efforts to mark them down as
‘inferior’. For example,adivasis(‘tribals’) and
dalits (the ‘oppressed’, or ex-untouchables)
in India have proclaimed their First Nation
status (seecaste). sco

Suggested reading
See http://www.atd.quartmonde.org

fractal Fractals are irregular objects that
cannot be defined by traditional geometry
but which, in some cases (such as Koch snow-
flakes) have the property of self-similarity:
their pattern appears the same regardless of
the scale at which they are viewed.
The easiest way to explain fractals is by
appeal to intuition. Incartographywe are
used to zero-, one- and two-dimensional
objects representing point, line and area fea-
tures on a map. Simply by looking, it is obvious
that each higher-dimensional object fills more
of the space than a lesser one: a rectangular
object fills more of themapthan a line placed
along one side of the rectangle or a point posi-
tioned at one of its corners. There is a connec-
tion between dimensionality and space filling.
Now think of a number line. Although we
often count using whole numbers (1, 2, 3,
... ), we also accept that the line is continuous
and so provides us with fractions (1, 1.2, 1.31,
1.411 etc.). Can the same principle be applied
to dimensions?
Various nineteenth- and twentieth-century
mathematicians have shown that it can. Of
particular interest to geographers is Benoıˆt
Mandelbrot’s (1967) question, ‘How long is
the coast of Britain?’ As he showed, there is no
one answer: it depends on the precision of the
measuring device – the calliper – used to trace
around the islands (seemeasurement). As the
precision increases, more of the detail of the
shoreline is included and the apparent length
increases.
To imagine the problem another way, sup-
pose that we could encode the coastline in
perfect detail in a digital mapping package
such as ageographic information system.
Each time we ‘zoomed in’ to a fixed location
on the coast more of its detail would be

revealed. This would happen every time, with-

out limit, because fractals possess infinite

detail. Of course, we cannot really encode

this infinite detail and so the total measured

length of the coastline becomes dependent on

thescaleof analysis – by how the coast is

generalized. Knowing this, we can take the

measurement at multiple scales, to plot the

(natural log) of the coastline length against

the (natural log) of the calliper used to meas-

ure it. The gradient of the line of best fit to

these values is an estimate of the coastline’s

fractal dimension.

This may sound abstract, but fractals are

evident innature: leaves, trees, river networks

and so forth. Their relevance is not just to the

physical landscape. Within the social sciences,

fractals can be used to model the processes of

urban morphology (Batty and Longley,

1994). Reciprocally, the fractal dimension, as

a measure of space filling, can be used to

model thesprawlor compactness of cities.

Fractals can be linked tochaos theory: the

idea that physical or social systems that appear

to be chaotic can actually be modelled by

clearly defined ‘laws’ or theories (e.g. using

economic theories to model urban develop-

ment and growth: see Batty, 2005). Finally,

fractals are used inremote sensingto com-

press (reduce the file size) of images. rh

Suggested reading

Batty (2005); Mandelbrot (1967).

free port Anenclavewithin a country –

typically a seaport, though increasingly other

areas – where import and export (customs)

duties are either not imposed or are reduced.

This enables both warehousing and manu-

facturing functions to be located there produ-

cing a local comparative advantage and

generating employment and wealth, at a cost

advantage over other locations (cf. export

processing zone). Free ports (such as

Copenhagen, Danzig and Hamburg) existed

in Europe until the mid-twentieth century,

and free port status was a foundation of

the economic success of Hong Kong and

Singapore. The concept has been adapted for

some airports – as at Shannon in the Irish

Republic – and was reworked into that of

the urbanenterprise zoneby the geographer

Sir Peter Hall in the late 1980s to promote

redevelopment in run-down industrial areas

through tax advantages. Special Economic

Zones (SEZs) with very similar characteristics

are now widespread in the global south:

India initiated a programme in 2000 and by

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