The Fractal Dimension of the Coastline as a
Determinant of Western Leadership in Science and Technology
(symposium "Fractals 2000 in Biology and Medecine",
11 Mar 2000)
This paper argues that the fractal dimension
of the Western European coastline was an important causal
factor behind the continent's tremendous success in science
and technology over the last centuries. The nicely articulated
coastline fostered the political and economic developments
necessary for science to flourish. These political and economic
conditions of scientific progress are briefly outlined here.
The fractal dimension is used as a means to precisely quantify
the coastline's degree of articulation. Measurements are
made in the 100 to 1,000 km range. Western Europe's
coastline is shown to have a significantly higher fractal
dimension than those of the Middle East, India and China.
Why did Western Europe succeed scientifically the way it did
during the last centuries? And why didn't other civilizations?
Why was modern science and the industrial revolution invented
by the West? I shall argue in this paper that the causality
chain leading to the European scientific "miracle" started
with the high fractal dimension of the Western European coastline.
The Western part of the European continent is the only densely
populated area on Earth boasting as many peninsulas, gulfs,
straits, inland seas, while still being for the most part an
Such an articulated coastline enhances trade, because sea
accessibility makes maritime transportation easier.
The sea route is much better than river or land transportation.
It is tremendously cheaper, it is less limited in capacity
and enjoys more freedom. Before modern times, it was even faster.
Thus a high level of coastline articulation, by bringing the sea
closer to all places, allowed the economy to thrive in the long-term.
An articulated coastline defines naturally limited core areas
(peninsulas, half-peninsulas, islands) within which polities
can live their lives without being too much disturbed,
as the sea is the best possible boundary for a state. Britain,
Spain, France, Denmark, Sweden are such ancient states,
well delimited by the sea. The shape of the Western European
coastline helped the continent to remain divided between
stable and long-lasting states.
Thus the Western European coastline shape most probably
enhanced economic growth and fostered the continent's
stable states system. We shall argue that this political
and economic background was the necessary and sufficient
condition for the flourishing of science.
[2/5] A Political and Economic Theory of Scientific Progress
A rich economy allows scientific and technical progresses
in many ways: It generates a surplus, necessary for science
and the arts to thrive. Moreover, merchants, bankers and
entrepreneurs are obsessively looking for accuracy,
counting, number-using. When successful, they gradually
impose their science-friendly mentality upon society.
Even better: merchants, bankers and entrepreneurs have
a vested interest in science and technology: they support
developments in mathematics (accounting arithmetic,
higher-degree equations for interest rate calculations,
statistics for stock exchange trading and insurances, etc.).
In the Middle Ages, they supported the development
of clocks for measuring manufacturing and travelling times,
of accurate maps for travelling, of astronomy for navigation,
and of course of all sorts of technical devices, since
increasing manufacturing productivity and decreasing
transport costs brings profit.
Stable political division helps science and technology in many ways.
It generates freedom. No center has a monopoly of power,
no government can control everything. The diversity of legislations
grants a much larger overall liberty to science. Suppressed
in a given country, a scientist or a technician can look
for shelter in another one (these effects were already identified
by various authors, like  and ). But there is more.
Competition between states generates a profitable stimulation.
Every government wants to do better (or at least not worse)
than neighboring countries. Hence governmental support for
science academies. War exercises a continuous pressure towards
modernization, it creates a strong government interest
for new technical devices and for improving technical knowledge
and education. But unfettered war wreaks havoc, thus the need
for stable political division.
The same holds true for the smart European scientific professional
structure: universities, royal academies, private schools
of mathematics. The institutions that allowed scientists
to make a living while doing research could come to life
only thanks to the good economic and political situation
of Western Europe. When studying their history, it is easy
to verify that these institutions thrived because of the
possibility to flee to a another state, the availability
of financial means, inter-state prestige and military rivalry.
Hence, we may formulate a general rule: in a given region
(we should look at a complete region a region mainly
isolated from major outside influences , i.e. a civilization
earlier, and the world nowadays), science and technology
can advance if and only if the region hosts a rich
and stable states system. Western Europe enjoyed a growing
trade and manufacturing, and was divided between long-lasting
competitive kingdoms during the whole 2nd millennium;
this is why it succeeded the way it did. Other civilizations
did not form rich and stable states system during as long
a period as Europe, that is why, on the whole, they had
less success in science.
[3/5] Eastern Europe and Other Civilizations
The rich states system theory explains quite well the
different stages of the scientific evolutions of Western
Europe, Eastern Europe, the Middle East, India and China.
As I showed in Le secret de l'Occident ,
each time prosperity and stable division are there,
science flourishes. Conversely, when other conditions
are rife, like political unity, fast-changing boundaries,
civil wars and/or economic doldrums, science recedes.
In particular, that theory sheds light upon the mysterious
drop of Chinese scientific development around 1300:
at this time, China departed from a "stable states system"
state towards political unity. China did not enjoy
favorable conditions again during centuries. It first
entered unity, then suffered a civil war, then fell
into unity again.
The difference between Western and Eastern Europe is
neatly solved as well.
The steadily weak performance of Eastern Europe
in science and technology can be linked to the bad economic
and political conditions which it suffered along
the 2nd millennium. Eastern European states were unstable,
they underwent fast boundary moves, they appeared
and disappeared. Trade was weak, manufacturing rickety.
Merchants never thrived half as well as their Western
equivalents. This can be linked to the fact that
Eastern Europe does not enjoy as good a shore profile
as Western Europe: it is a mainly landlocked area.
Vast surfaces are deprived of sea access: the seas are
too far away and are often closed or ice-blocked.
The vast land compactness explains why the economy
remained sluggish (sea trade could not play a role)
and why the region's states were brittle and
short-lived (no natural boundary protected them).
[4/5] Measuring Fractal Dimensions of Coastlines
4.1 Indices to assess a Coastline
The quality of a coastline (its degree of indentation)
can be quantified with various indices, which we shall
briefly compare here.
A very simple procedure is to measure the distance
to the sea of the farthest point inland. This measurement,
a first indication at best, gives the best note to
Western Europe (see table).
Another, more elaborate, method consists in measuring
the coast length and dividing it by the surface of
enclosed land. This is the so-called
"coastline development index". We display in the table
below the results obtained by using shoreline measurements
from Lucchini & Voelckel . The development index
sets Western Europe far above, at first rank.
The development index, however, is not a completely
satisfying quantity because the length of the coastline
is no definite quantity. A coastline actually is a
fractal object, with no upper bound on its length.
Comparison between development indices makes sense,
to a limited extent, only so far as the coast lengths
were measured at identical scales. The degree
of articulation of the coastline is best measured
by the fractal dimension.
To measure coastlines fractal dimensions, we relied
on the Richardson technique (see e.g. ), which
originally inspired B. Mandelbrot in its exploratory
work on fractals.
The length of the coastlines of Europe, the Middle East,
India and China were measured on the map with a compass
of an aperture of 1,000 km. The compass approximated
the shoreline with a broken line, whose length could be
easily measured. The same operation was repeated
with smaller and smaller segments. The segments varied
between 1,000 km and 100 km.
The lengths of the broken lines were plotted versus
segment lengths in a logarithmic-scale graph. The slope
of the curve was taken as the fractal dimension.
It was thus an "intermediary" fractal dimension,
i.e. taken within a given segment range, and not the
fractal dimension according to the mathematical definition,
where one should look for the limit when segments shrink
to zero, i.e. at the slope of the logarithmic curve
in the graph at infinity.
The justification is the following: first, in a natural
object like a coast, there is no guarantee that the slope
of the logarithmic curve will converge to a defined limit.
Second, when looking for factors impacting long-term
history, we judge the 100-1000 km range much more
relevant than, say, the millimeter or micrometer ranges.
For each civilization, a start point and an end point
were defined for the measurements on the map. The length
of the broken line was defined as the number of entire
steps plus the remaining length up to the end point.
The broken line follows the continental coastline.
Islands receive separate broken lines as soon as they are
large enough for the segment to "see" them. In such cases,
a start and an end points have to be chosen for the island,
introducing some arbitrariness in the process.
To reduce this arbitrariness, we aimed at maximizing
the measured length at each segment scale. Island coastline
lengths were added to the continental length.
Sometimes, the segment has the choice between two
intersections on the map.
For example, at the "heel" of Italy, the 316 km segment
sees both the Italian Adriatic coast and the Greek coast.
In such cases, preference was given to the closest point
along the coast, i.e. the one maximizing the final measured
An alternative calculating method to assess fractal
dimensions would be to include terrestrial domain
borders. These non-maritime border lines would be
considered non-fractal, bringing a constant kilometer
add-on on each shore length measurement.
This approach would better mirror the impact
of large terrestrial areas with little access
to the sea, like Central Asia, which are not "seen"
with a compass sticking to maritime borders.
It would lower the final fractal dimension of
terrestrial areas, yet increasing the Western European
Be it for deriving fractal dimension, maximum distance
to sea, or coastline development, the four regions
to be compared (Europe, Middle East, India, China)
were defined as follows:
"Western Europe" includes all territory west
of the line Lubeck-Venice, with the Swedish-Norwegian
peninsula added. "Western & Central Europe" contains
all of European territory except the pre-1990
Soviet Union and Finland.
"The Middle East" was defined as Africa north of the
Sahara, Arabia, Mesopotamia, Iran and Central Asia.
The Southern limit was the Sahara desert around
present-day boundaries of Morocco, Algeria, Lybia
and Egypt. The Northern limit was the Caucasus
and Anatolia. Central Asia has only terrestrial
limits. The starting point of the first coastline
was in Southern Morocco, ending at the present-day
Syrian-Turkish border. The second coastline was
that of the southern Caspian sea. The third coastline
started on the Sudanese coast and ended at the
starting point of India.
"India" was defined as the whole Indian subcontinent.
That includes present-day Pakistan, Republic of
India, Bangladesh, Nepal, Bhutan, Sri Lanka, Maledives,
Laccadives. The start point was near present-day border
between Pakistan and Iran, on the west of the Indus
delta. The end point was on the Eastern side of
the Gange delta, within present-day Bangladesh.
"China" was defined as the area populated by Han until around
1700. This includes the present People's republic of China
without Manchuria, Inner Mongolia, Eastern Turkestan
and Tibet. The coastline extended from Tianjin
(harbor of Peking) down to the present Vietnamese border.
Taiwan and Hainan were included.
The length of the coastlines was successively measured using
1,000 km, 316 km, and 100 km segments,
so that the corresponding points were equally spaced
in the logarithmic space. More segments can anyway be added
inbetween if wished. A graph was built plotting increasing
coastline length versus decreasing segment length. A best fit
for the slope was obtained. This slope was dubbed the
"intermediary fractal dimension" in the range 100-1,000 km.
[5/5] Results and Conclusions
The results of different coastline measurements are displayed in the table below.
Max. dis-tance to the sea (km)
Deve-lopment indice (10^-5 km/km2)
"Inter-mediary" fractal dimen-sion
Western & Central Europe
Table: quantifying the articulation/ indentation
of the coastline
The results clearly show that Western Europe
has a much higher fractal dimension (1.47) than
China (1.26), India (1.19) and the Middle East
(1.12). These differences are significant because
these figures can take values between 1 and 2,
theoretically. Practically, they vary in an even
narrower range. Indeed, a coastline with a
fractal dimension as high as, say 1.8 or 1.9,
is barely thinkable.
Thus, what is seen with the eye is confirmed by
quantitative measurements. Western Europe boasts
a much more articulated coastline than other
civilizations. It has several large peninsulas
(Spain, Italy, Denmark, Sweden-Norway), several
islands more than 100 km wide (Britain, Ireland,
Iceland, Sicily, Sardinia, Corsica, Sjaelland,
Gotland). Whereas the Middle East just has
nascent peninsulas (Tunis, Byrte) and no large
island. India has only one peninsula (Gujarat)
and one large island (Ceylon). China has only
one peninsula (Shandong) and two islands (Taiwan,
The intermediary fractal dimension tell the same story
as the other indices tested. Western Europe has a
much more indented coastline than other civilizations.
This geographical factor, through a complex chain of
political and economic causalities, might have given
Western Europe its edge in science and technology during
the second millennium. Hence, although surprising at
first sight, the European scientific "miracle" seems
to be, indirectly, a present from geology.
 Braudel F., Civilisation matérielle, économie
et capitalisme (XVe-XVIIIe siècle), Armand Colin,
 Jones E., The European Miracle. Environments,
Economies and Geopolitics in the History of Europe
and Asia, Cambridge University Press, Cambridge
 Cosandey D., Le Secret de l'Occident,
Arléa, Paris (1997).
 Lucchini L., Voelckel M., "Les Etats et la mer,
le nationalisme maritime", in:
La Documentation française (1977), citant des
chiffres du Geographic Bulletin, no3, oct 1969.
 Gerald E., Classics on Fractals, Addislon-Weslex,
Reading, Massachussetts, Etats-Unis (1993).