REFERENCE:
Journal of Mathematical Modelling and Application
2011, Vol 1, No 5
ISSN: 2178-2423
Journal of Mathematical Modelling and Application
2011, Vol 1, No 5
ISSN: 2178-2423
Abstract
It is very difficult to define what ruins are, by definition,
irreparable remnants of human construction by an act or destructive process. We can not talk about them as
objects, even though we know that one day buildings reach their end, the
question is on how to reach this final. Fragment causes mental associations with the person who perceives, that
happens to be a mystery, since no one knows the facts that have been associated
with the final ruins. However, the mental reconstruction is not
straightforward, because the ruins interact with nature, are absorbed by it,
change over time. This is our aim to show this dynamic situation in which man
intervenes in the reconstruction, by a mathematical analysis of the city of
Nagasaki based on fractal geometry, and evaluate if there is any related urban
morphological pattern before and after the bomb. The method applied is Box
Counting.
Keywords: City reconstruction; Fractal geometry; Box
counting method
Introduction:
A Brief History of Nagasaki
Nagasaki was founded before
1500, as a modest harbor village. In 1542, a Portuguese ship accidentally
landed nearby allowing the first contact with European explorers. In years, the
city grew into a port city. Nagasaki became a free port in 1859, with ship
building as the main industry. Since many Japanese warships were built in its
factories and docks, the city became a target for the detonation of the second
nuclear bomb, in August 9th 1945.
Among other considerations,
the target of Hiroshima and Nagasaki was selected because of the expectation to
produce the greatest amount of damage by primary blast effect plus fires. The
maximum blast effect of the bombs was calculated
to extend over an area of approximately 1 mile in radius.
Description of Damages
Adapted
from The
Atomic Bombings of Hiroshima and Nagasaki. By The Manhattan Engineer District. June 29, 1946, we reproduce this basic data to
understand the plain aerial view in the aftermath of the bomb:
All Japanese homes were destroyed within 1 1/2
miles from X, being X the very target. 1500 feet from X, high quality steel
frame buildings were not completely
collapsed, but the entire buildings suffered mass distortion; 2,000 feet from
X, reinforced concrete buildings were collapsed; brick walls were completely destroyed; multi-story brick
buildings were completely
demolished. Similar buildings were destroyed to 5,300 feet.
The
actual collapse of buildings was observed at the extreme range of 23,000 feet from X in Nagasaki. 14,000 or 27%
of 52,000 residences were completely destroyed and 5,40O, or 10% were half destroyed.
Reconstruction
After
the bombing, people began to put up precarious huts to live in, using the
materials collected from the collapsed buildings. Housing
construction commenced in 1946. The reconstruction of Hiroshima and Nagasaki
was very slow, despite the efforts of the cities´ governments. There was not
enough money to pay for the materials and the workers. In
1949 Nagasaki was declared by the Japanese
Parliament ¨The City of International Culture¨ and was granted a sum of money
for the reconstruction. (Langley, p. 79)
Though a slow process, the post war period saw the
gradually increase in independent citizens´ organizations and movements which
had profound effects on the city´s development and on the urban planning system
(Sorensen, p. 154). Special rules had to be established for suburban areas with
a mixture of urban and rural uses. Town planning was decentralized and projects
were the responsibility of municipalities with citizens´ participation. Urban plans
were based on the Tokyo Earthquake reconstruction project. There were new
standards for buildings, lot coverages and 10% of the urban area was destined
to parks and the designation of greenbelts to avoid sprawl. New grand avenues
were open to accommodate future motorization. The
result was a ¨modern¨ urban pattern, but based in the 1919 city planning system
(Sorensen, p. 159) with its real limitations.
Large
areas of land on the fringe were zoned residential or industrial, but without
any powers to guide urban design or development standards, and future patterns
of development were largely at the discretion of landowners¨. (Sorensen, p.160)
Methodology
Our objective is to
analyze the urban morphologies of the City of Nagasaki along the years, and see
if there was any hidden similarity among them, though urban patterns are very
different at first glance. If so, we can state that a cultural-psychological
behavior has been kept even after a catastrophe, reflected in the urban
pattern.
In
Euclidean mathematics two geometrical objects are called similar if they both have the same shape, precisely, if
one is congruent to the result of a uniform scaling of the other. But, while
applying a fractal analysis, we understand similarity
in its broad sense and the only scaling we are considering is based on
iterations. We can go further and see if they also have auto similarity.
As we see in the aerial picture of old Nagasaki, there
was no urban Euclidean pattern, houses were spread with no planification, areas
cut up by hills and mountain, with no regularity. To find out the Fractal
Dimension, we used the software ImageJ and followed these steps:
Enhance the
aerial picture giving more contrast and sharpen the edges
Find edges and
transform into a binary file
Calculation of
the Fractal Dimension with the Box Counting Methods.
The aerial
pictures after the bombing and reconstruction under planning regulations were
treated under the same steps and method.
Results
One
of the main property of fractals is auto similarity. All structural conditions
are the same all through different scaling. The simplest example is the
cauliflower, each flower inside is auto similar to the main flower. They keep the same properties.
Once
the system is affected by an external issue (in this case, the bomb), the
fractal pattern as a geometrical representation, could be changed. We divide
the urban pattern in three: before-after the bomb and current. With the results
below we are able to demonstrate that they have very similar values for the
fractal dimension D, it means rugosity and urban fabrics –open vs filled
space-, the same ratio values in land occupancy before and after the bombing,
even when the land was devastated. In other words, the form of the rebuilt city
could be different, but its fractal pattern appears to be the same, for the
reasons we discuss later.
The
software allows us to see the box counting at each iteration (I) with auto
similarity in each case:
Discussion
Regrettably, while working on this paper, Japan has
suffered from another catastrophe due to the terrible tsunami of 8.9 magnitude
temblor near the East coast, that killed thousands of people and engulfed
entire towns. And the attitude of the citizens kept alive helps us to
understand if there was a cultural behavior in these two events separated by
long years. We have seen above that after the bomb, there were independent
citizens´ organizations and movements which had profound effects on the city´s
development and on the urban planning system, due to lack of money or failure
at administration processes. In consequence, people began to build without the
authorities´ control, what finally was materialized in a complex urban pattern.
Progress in our research, tells us that there is also a psychological reason
that makes the citizens work alone: ¨The only
country ever hit by a nuclear attack, Japan has a visceral appreciation of the
uncertainties of radiation exposure, how it can spare some people in its wake
and poison others silently, causing disease years later. (…)
Compounding the problem, Japanese psychologists say, is that many of their
countrymen will attempt to manage their anger, grief and anxiety alone. (…) The quake, tsunami and radiation have destroyed or
defiled what may be the islands’ most precious commodity, land, dealing a
psychological blow that for many will be existentially disorienting. “In rural
communities especially, there’s a very strong feeling that the land belongs to
you and you belong to it,” said Kai Erikson, a sociologist at Yale who studied
mining towns of the Buffalo Creek hollow in West Virginia, where more than a
dozen towns were destroyed and at least 118 people killed when a dam burst in
1972, unleashing a wall of water as high as 30 feet that swept down the hollow.
“And if you lose that, you’re not just dislocated physically, but you start to
lose a sense of who you are.” (Carey, New York Times, march 2011)
Conclusions
¨Insofar as the
statements of geometry speak about reality, they are not certain, and insofar as they are certain, they do not
speak about reality¨. (Einstein, 1921, p. 3.)
Fractal geometry has emerged as a direct solution to
the need for more accurate mathematical descriptions of reality, and no doubt
it is a powerful and appropriate tool for interpreting complex systems,
impossible to see under the light of Euclidean geometry. D (Fractal Dimension)
quantifies concepts in terms of shape, texture, size, quantity, color,
recursion, similarity, regularity, heterogeneity, roughness, and other
properties of the urban fabric. In principle, we can say that the original
urban fabric of Nagasaki, unplanned, somehow reflects the private actions that
have not strictly followed the guidelines of the postwar planning. With respect
to the image of Nagasaki affected by the bomb, the software analyzes particles
too, and this is the most curious aspect of the analysis, since we only see the
ground zero. However, there must be progress on other morphological features
studies, since D is not the only parameter, and there are other analytical
methods, like Cellular Automata, Dynamic Urban Evolutionary Model, Percolation
systems, and one of the most important to discover hidden structures, the
Fourier transformation. (FFT) The subject developed over these pages approaches
us to the problem of urban theorists, who, from the social-psychological field,
have found the visual paradigm empty for the purpose of studying the
socio-historical processes. We tried to
open a new perspective in considering the impact of the physical determinants
of them. In this regard, Japan is an unique example of urban
development after the bombs.
The comparison above with an American town, is not
enough to prove that rebuilt urban patterns will show the same fractality
everywhere in similar conditions, also we should consider that Japanese people
has distrusted that the government is telling them the whole truth about the
nuclear events. Neither the earthquake, nor the tsunami that followed, nor days
without electricity, water or heat could drive people from their home, except
for radiation. (See Fackler, New York Times, march 2001). That is for us a
strong cultural tendency, the aim to go back and keep one´s dwelling as it
originally has been.
A comparison with the Chernobyl disaster is not
possible also, because the area is in an Exclusion Zone controlled by the
Administration of the Alienation Zone within Ukraine's Ministry of Emergencies
and Affairs of Population Protection from Consequences of Chernobyl
Catastrophe. Inside this area, buildings are abandoned, as residential,
civil or commercial activities in the zone are prohibited.
As a preliminary approach, we would state that
Japanese people has done much better than Russians. UN through the Chernobyl
Programme believes that ¨The evacuation of hundreds of thousands of people,
particularly from less contaminated areas, is seen as an over-reaction, which
in some cases did more harm than good. 'The first reaction was to move people
out. Only later did we think that perhaps some of them shouldn't have been
moved. It has become clear that the direct influence of radiation on health is
actually much less that the indirect consequences on health of relocating
hundreds of thousands of people,' Among relocated populations, there has been a
massive increase in stress-related illnesses, such as heart disease and
obesity, unrelated to radiation. (Browne, Guardian.co.UK, January 6th
2002)
We consider that while the research continues and
years pass by to understand and improve the results, the application of a new
order based on fractality is the answer we propose to the phrase of the worried
Einstein quoted here.
Acknowledgments
This paper is based on
the author´s extensive research on fractal urban morphology, which has been
supported for years by softwares that can be downloaded from laboratories
around the world, many times for free. The author is thankful for being able to
contact all the softwares´ designers for every specific question that emerged
during her research.
References
Browne, Anthony. ¨Myth¨ of Chernobyl suffering
exposed. Guardian.co.UK. Section The Observer. January 6th 2002
Carey, Benedict. Lessons for Japan’s Survivors: The
psychology of recovery. Published at the New York Times, Section “ The Week in
Review”.March 19th 2011.
Fackler, Martin. Radiation Fears and
Distrust Push Thousands From Homes. New York Times, section Asia Pacific. March
17th 2011.
Langley, Andrew. Hiroshima and Nagasaki: fire from the
sky. White-Thomson Publishing Ltd. USA. 2006
Manhattan Engineers District. The atomic bombings of
Hiroshima and Nagasaki. Report of June 29th, 1946.
Sorensen, André. The
Making of Urban Japan: Cities and Planning from Edo to the Twenty First
Century. The Nissan Institute/ Routledge Japanese Studies, London, 2004
