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Universiteit Leiden – Faculty of Governance & Global Affairs.
MSc Crisis and Security Management.
Master Thesis.
Fractal Theory and the Time invariants of a crisis; a case study approach.
Student: Hannah Wren
Student Number: s1826557
Supervisor: Wout Broekema
Second Reader: Ruth Prins
Date of Admission: 09/01/2018
Word Count (Excluding Bibliography, Appendix and Front pages): 19,964
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Acknowledgements
I would like to thank my supervisor, Wout Broekema, for guiding me and all the support
provided throughout this thesis writing process.
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Contents
Chapter
Page
Introduction
4
Theoretical Framework
9
Methodology
20
Analysis
33
Summary of findings
48
Conclusion
50
Bibliography and sources used
53
Appendix
60
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Introduction.
With the nature and frequency of crises constantly changing, crisis management needs
to adapt to deal with the new challenges that are presented. ‘Best practices’ have been created
and used over the recent years to react to the outcome of crises (Fink 1986; Ten Berge 1990).
However, these practices no longer hold true, “the need for a decisive breakthrough appears
crucial in the present world, where crisis is no longer the marginal but the core engine”
(Topper and Lagadec 2013: 5). “Crises are our new reality. ‘Black Swans’ are increasingly
becoming our norm” (Topper and Lagadec 2012: 21). The need for a change in perspective
and attitude to crisis management has become evident. Modern crises do not limit themselves
to a specific category or area of policy but encompass many aspects, to create “Unforeseen
mega-threats” (Boin 2004: 166). With the changing nature of crisis management, a
fundamental aspect from traditional crisis management remains “our planet has become ‘a
world at risk’” (Rosenthal, Charles and T’Hart 1989: 3).
The problem that this research aims to tackle, is that of how best to respond to crises
and to determine whether there are any aspects of crisis response that repeat. This would
enable a better prepared, structured response when a crisis does strike. This research will be
an explorative study to determine whether there are repeating patterns of actions in Time
(Fractals) that appear in all of the nine cases that have been selected across the three crisis
types; Man-made, Natural and Technical Failure. Topper and Lagadec (2013) are the first
academics to apply the notion of fractals to crisis management. They are key pioneers for
Fractal theory and therefore their previous research is the main foundation for this research.
Fractal theory is relatively new in its application to crisis management. Therefore,
there is opportunity to utilise the ideas and notions suggested by Topper and Lagadec (2013)
to determine its relevance and usability within crisis management. Topper and Lagadec
(2013) are the first crisis management theorists to implement or suggest this shift in
perspective to one of fractals within crises. Consequently, this is the first time Fractal theory
has been used within Crisis and Security Management. No other academics have applied or
utilised fractals and Fractal theory within the field of crisis management, therefore this
research focuses solely on Topper and Lagadec’s (2013) theory. Topper and Lagadec (2013)
aim to “initiate new thinking, innovative perspectives for the field of crises” (Topper and
Lagadec 2013: 10). The overall goal being to “renew crisis management theory” (Topper and
Lagadec 2013: 10). With crises becoming increasingly complex, the need to adapt and
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change crisis management theory from its traditional setting to a more current application is
required. The use of fractals outside of a mathematical or economic context is relatively rare,
even more so within crisis management. Therefore, this use of fractals by Topper and
Lagadec (2013) to underpin a crisis management theory, provides a new opportunity to
research and better understand the structure of crisis response. Fractals are not commonly
known outside the sphere of mathematics and economics, so it is important to have a clear
understanding of what a fractal is prior to the research commencing. Fractals are repeating
patterns that increase and decrease in size and are identical no matter the size. Fractals can be
defined as
“A curve or geometrical figure, each part of which has the same statistical character
as the whole. They are useful in modelling structures (such as snowflakes) in which
similar patterns recur at progressively smaller scales, and in describing partly random
or chaotic phenomena such as crystal growth and galaxy formation” (Oxford English
Dictionary 2017).
Topper and Lagadec (2013) utilise this notion of identical repetition and apply it to
crisis response and crisis management. Within their Fractal theory there are four main
invariants/aspects which are highlighted as key features that are prevalent in all crises and at
all levels/scales of the crisis response. These are Space, Time, Rank and Sense-making. Due
to the limited conceptualisation provided by Topper and Lagadec (2013), this research will
only focus on one of these invariants: Time. This is to increase the feasibility within the time
frame permitted for this research, whilst also including the most amount of aspects from
Topper and Lagadec’s (2013) theory framework. This enables a more structured and accurate
examination of time within crisis management. Once this structure is created it can be
applied to future research into the other three invariants. Limiting the research to the study of
Time also increases the detail in which Time can be analysed as an invariant within multiple
case studies, increasing the opportunity to determine the legitimacy of the Fractal theory
within differing types of crises. Time has been isolated within this research as the invariant to
be analysed as it is a physical construct which is measurable. Similarly, Time is easier to
conceptualise than Space, Rank and Sense-making enabling the process of creating a
structure with which to analyse the invariants less complex. In future research the structure of
this research will be applicable to the remaining invariants. Equally Time will be less
complex in identifying repeating patterns, which will increase the validity of the research as
the components will be more visible within the case studies. This use of just one invariant
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analysed in depth “allows for more powerful tests to establish generic mapping of crisis”
(Topper and Lagadec 2013: 12) which creates a structure for the three other invariants to be
analysed against.
The scientific relevance of this research has its foundation in the limited use of Fractal
theory in any prior crisis management research. Fractal theory has not been applied to crisis
situations in a real context before. There are numerous reasons for this not being applied
before with the main one being the vagueness of the terms provided by Topper and Lagadec
(2013). This will be remedied by applying specific interpretation, with clear and explained
definitions, determined prior to advancing further into the research. The research will seek to
add to the theoretical debate surrounding crisis response, especially regarding the similarities
between crises and crisis response. This research will be academically relevant as it will
increase the knowledge surrounding crisis management and add to the understanding of
fractal theory when hindsight is applied to crisis situations. As traditional crisis management
is becoming less applicable, and the nature of crises is changing, a more modern method of
crisis management is needed. As Fractal theory was only applied to crisis management in
2013 the theory is relatively new. This research will increase the understanding of Fractal
theory and its practical applications in a crisis setting. Topper and Lagadec (2013) go so far
as to acknowledge the shortcomings in their theory “we are only at the beginning of the
intellectual brainstorming required by the age of mega crises” (Topper and Lagadec 2013:
15). Therefore, it is important to proceed with caution due to the limited availability of
further information on Fractal theory. This increases the importance, value and academic
relevance of this research. Topper and Lagadec (2013) even call for further research into
fractal theory within their own research; “on the research agenda, we will modestly plead for
launching research projects” (Topper and Lagadec 2013: 15). Creating an understanding of
the Time fractals within crisis response will be scientifically relevant, as it will contribute to
filling the knowledge gaps surrounding patterns within crisis response and the best course of
action that is required to achieve the most effective outcome of crisis response. This research
is in response to Topper and Lagadec (2013), adding data to the niche gap within crisis
management, and increasing the applicability of Fractal theory in practical crisis situations
and analysis. This new perspective on crisis management provided by Topper and Lagadec
(2013) will potentially provide different and creative ways to respond to crises.
With new types of crises on the rise and the prevalence of transboundary crises on the
increase, a form of managing new types of crisis can improve and adapt management of
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future crises. The research will be socially relevant as it will highlight new ways of
understanding crisis response and may impact the practical aspects of crisis management,
including preparedness. Understanding common occurrences during a crisis will increase the
practical aspects which can be put into procedure, response and recovery. “In crisis situations
decision makers have great difficulty in redefining the situation and thus tend to stick to a
dominant course of action” (Rosenthal, Charles, T’Hart, Kouzmin and Jarman 1989: 467).
As the nature of crises change so do the needs and skills of responders; “We must visit the
new frontiers with confidence, improve our intelligence about them and acquire brand new
skills – vision and an entire strategy logic. In order to remain actor of our particularly
turbulent period of history.” (Lagadec 2006: 507). Therefore, increasing the understandings
of the patterns and invariants within a crisis can change the options and actions of responders
and decision makers. This research will challenge the norms and supply a new perspective in
crisis response. The exploration of the Time fractals within a crisis will improve the
understanding of the structure of crisis response, which can potentially impact policy strategy
and preparation for the planning crisis response.
This research aims to apply the Fractal theory put forth by Topper and Lagadec
(2013) to case studies, to determine the Time aspects of the crises that have remained
constant at all levels of the response and recovery. The cases used in this research will be
grouped into Man-made, Natural and Technical Failures. Within these groups three of each
type of crisis will be analysed. All the cases selected occurred during or after 2000, which fits
with the ideology of Topper and Lagadec (2013). Modern crises need a modern crisis
response and management style. As all the crises occurred within the last 18 years, relevant
documents are easily accessible. All the crises occurred in developed countries, which
increases the validity of the results for developed countries. Further research will be needed
to determine the validity within less developed countries. All the cases occurred within
countries which have the means and economy to provide an acceptable crisis response, and
provide investigations and reports following the crisis. They also cover a wide variety of
cases within each type category allowing for an increased validity in the finding as the range
of crises is greater. Similarly, as the cases are from four different continents the results should
provide a clear example of whether fractals are an integral part of crisis response for crises in
developed countries. As the nine cases are from a variety of countries, the culture of crisis
management and how the crisis is responded to will be different. Using cases from different
countries mitigates the potential for culture as being the driving factor in fractals rather than a
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universal fractal within crisis management. The cases selected cover a wide selection of
crisis events within each typology of crisis. Therefore, this spread of cases provides a
variation in responses needed for each case, enabling a more accurate determination of the
applicability of Fractal theory on all crises. All the crises have high quality and reliable
documents to support the research and uphold the integrity of the research. Alongside this, all
the documents are easily accessible and in English, increasing the feasibility of the research.
This provides a better chance of understanding the role and impact of fractal theory in crisis
situations and its applicability to differing type of crises.
The research question that this research aim to answer is: To what extent do different
types of crises, individually and collectively, demonstrate Topper and Lagadec’s (2013)
Fractal theory, specifically with reference to the concept of Time?
The research will seek to understand the Time invariants of the crisis from a Local,
Regional and National viewpoint based on Topper and Lagadec’s (2013) Fractal theory. The
emphasis will be on the Time invariant of each crisis case study. Therefore, the research
question is supplemented with 2 guiding sub questions:
- What are the types of crises (Man-made, Natural and Technical Failure)?
- What are the Time invariants/fractals present in the crisis?
These sub questions will contribute to the research question and will increase the clarity of
the results. The sub questions will be applied to increase the understanding of fractal theory
and enable the Time invariant to be clearly isolated within the crises. Similarly, the sub
questions provide a background of information which will support the main research
question.
In the coming chapter, the theoretical framework and background for Fractal Theory
(Topper and Lagadec 2013) will be discussed, alongside a detailed systematic breakdown of
crisis management and crisis response. After starting with the broad context of traditional
crisis management, the following theoretical aspect will be discussed; types of crises, fractals,
response levels and invariants. This is followed by the methodology which will be used to
analyse and observe Fractal theory in crisis situations. The analysis will follow, including a
brief background to each case, explaining what occurred in the immediate aftermath of the
crisis event. The analysis will detail the Time invariants within each crisis response and a
discussion of the findings and concluding remarks.
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Theoretical Framework.
Crises are times of instability and vulnerability where actions and responses are often
necessary (Devlin 2007). Crises are difficult to define with many definitions provided, and
covering a range of different situations. They can be defined as “sudden, unexpected,
surprising and unpredictable” (Roux-Dufort 2007: 107). Roux-Dufort and Lalonde (2013)
describe crises from a psychological perspective of the individuals involved: a “crisis is seen
as a discontinuity from a previous dismantling equilibrium to another emerging one”
(Roux-Dufort and Lalonde 2013: 2). This is a vague definition and can be applied to many
situations. Whereas Topper and Lagadec (2013) describe a crisis as a “wild and maverick
reality, impossible to understand and grasp within frameworks shaped, built and stamped to
contain stable and repeated phenomena” (Topper and Lagadec 2013: 8). This understanding
of crises as an unexplainable singularity highlights the randomness and unpredictability of
crises. Current crisis theories focus on response strategies and the situations surrounding
crises with a top down command and control perspective of communication (Moynihan
2009). A top down approach to crisis management can be problematic due to lack of ground
level understanding in relation to the situation and the actions that are necessary, a new
perspective is needed to improve crisis response. Topper and Lagadec (2013) argue that the
current paradigms within crisis management are no longer adequate in creating understanding
of and theoretical frameworks for crisis management. “Crisis management cannot be a series
of fixed, easy to teach and apply ‘best practices’” (Topper and Lagadec 2012: 22). The use of
‘best practices’ has become a common tool in analysing and responding to crises (Topper and
Lagadec 2012). The nature of crises and crisis response is changing, which impacts the policy
process and emergency response in dealing with crisis management (Boin 2009). “Crisis
operations are multiorganizational, transjurisdictional, polycentric response networks. They
demand lateral coordination, not top-down command and control” (Boin and T’Hart 2003:
547). This lack of structure to crisis response is a contributing factor to how successful or
unsuccessful a crisis response is managed. Also, the locations of crises are becoming
increasing international and across multiple borders and effecting people from different
countries to that of the epicentre of the crisis (Boin 2009). As globalisation has increased the
mobility of individuals, the international impact of crises is becoming more prevalent. The
more traditional ways of crisis management may no longer be applicable to a multinational
crisis, and therefore “Development and management of past crises may have limited value for
improving the management of tomorrow’s crises” (Rosenthal, Boin and Comfort 2001: vii) as
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the nature of crises have changed. It is important to find and use new techniques for
managing crises. Boin and McConnel (2007) argue “the established ways of organising for
critical decision making will not suffice in the case of a catastrophic breakdown” (Boin and
McConnell 2007: 50) therefore a paradigm shift in crisis management theory needs to occur.
Traditional Crisis Management.
Traditional crisis management falls under the sphere of disaster sociology, with the
aim of conceptualising ‘disaster’ (Quarantelli 1998). Whilst a singular concept of disasters is
problematic there are characteristics which equate to a disaster; “core conceptual elements of
threat, urgency and uncertainty” (Boin 2009: 368). A traditional definition of a crisis is “a
serious threat to the basic structure or the fundamental values and norms of a social system.
Which under time pressure and highly uncertain circumstances necessitates making critical
decisions” (Rosenthal et al. 1989: 10). The inclusion of norms and values under threat has
become less obvious in more recent crisis management theories and definitions. Tierney
(2007) argues that disaster sociology originated from a realist perspective and that “disasters
represent the juxtaposition of physical agents (earthquakes, hurricanes, tornadoes, industrial
accidents) with vulnerable places and populations” (Tierney 2007: 506). This is a basic
definition of crises and is quite limiting in factors that both cause and are affected by crises.
Similarly, “Crises were viewed in functional terms as facilitators of long awaited change;
crisis management was interpreted as a mechanism towards the restoration of normalcy”
(Rosenthal, Boin and Comfort 2001: 5). Crises within traditional crisis management are
perceived as abnormal and unique events that disrupted the normality of everyday life. Also,
crises were “easily demarcated in time and space, and if necessary, easy to hide from the
outside world” (Rosenthal et al. 2001: 5). In a world where there was limited international
fall out from crises, limits were placed on the spread of damage caused. As the world has
become more globalised and internationally interdependent, shifts in crisis management and
paradigms of crises has had to adapt. A change in the paradigms surrounding disasters and
crises can be described as a change in consequences; “threat agents will look familiar (E.G.
natural forces, violence, and technological failure), but the consequences play out very
differently” (Boin 2009: 367). Crises have become increasingly transboundary, which brings
about new challenges. Transboundary crises extend beyond geographical borders, “jump
functional boundaries … from one sector to another ... transcend traditional time boundaries”
(Boin 2009: 368). Rosenthal et al. (1989) argue that the role of crisis management is
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7). Whilst crises are now increasingly transboundary (Boin 2009), the notion of a changing
nature within crisis management can be seen in the description of a ‘modern’ crisis portrayed
by Rosenthal et al. (1989). A ‘modern’ crisis is an event “where the action of one country can
have a dramatic impact on the populations outside the contiguous borders of a singular
nation” (Rosenthal et al. 1989: 3). The definition of a crisis has changed and adapted from a
traditional crisis management perspective to one that is more open and with a lesser focus on
the social impacts and more towards the international and physical impacts.
With crises on the increase, new methods of management are key. “Crises are no time
to reorganize adequately operating response systems, much less try to implement wholesale
organizational changes” (Van Wart and Kapucu 2011: 509). However, we can learn from
crises and implement the lessons during the response to the next crisis. Furthermore, crises
are perceived as abnormal, even though they actively shape and dictate our daily lives. A new
approach to crisis management is necessary, one that considers the constant similarities and
non-varying aspects of a crisis (Topper and Lagadec 2012). “In a world where complexity
and crises have become so dramatic and so frequent that they cannot be excluded as simply
marginal” (Topper and Lagadec 2012: 23) it is now important for crises to be treated as the
norm to identify features that do not vary so that they can be prepared for and counter actions
planned. The actions and aspects related to responding to crises can be transferable, with
aspects of crises remaining the same or at least somewhat similar (Othman and Beydoun
2010). These similar, repeating and non-varying aspects can be called invariants. Invariants
are aspects which do not change, “what is invariant from one state to the other and what can
be undertaken to better prepare and manage upcoming crises” (Topper and Lagadec 2013:
11). The search for invariants involves looking for and identifying “elements that are
common in different crisis events, it also means being able to understand what remains
unchanged” (Topper and Lagadec 2013: 11).
Types of crisis.
Applying typologies and classifications to crises can be seen as attempting to maintain
a measure of control over the situation through the ability to identify the threat (Gundel
2005). Traditional crisis management provides two typologies of man-made and natural
(Rosenthal and Kouzmin 1993). These distinctions are quite basic in their definitions and
assumptions of the crisis. Separating all crises into just two categories is quite limiting. In
contrast, if too many distinctions are made between types of crises the outcome is somewhat
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abstract and can overcomplicate crisis management (Rosenthal and Kouzmin 1993). The use
of common characteristics and features to categorise crises provides a useful framework in
separating and determining types of crises (Gundel 2005). Gundel (2005) suggests four
categories of crises all of which are centred around the notion of predictability and
influences; unexpected, intractable, fundamental and conventional. Whilst these
characteristics can help identify aspects of a crisis, they are subjective and can
overcomplicate the identification and organisation of crisis types. Similarly, Rosenthal et al.
(1989) argue that the type casting of crises is dependent on three aspects; crisis creation,
crisis preparation and crisis aggravation, which ultimately leads to six categories of crisis:
unimaginable, neglected, unavoidable, compulsive, wanted and wilful. These offerings of
grouping and categorisation are all highly subjective with limited clarity. The vagueness
surrounding these groupings do not provide much clarity, increasing the difficulty in
determining crisis type. Therefore, these categories will be used to further the understanding
surrounding crises but not used further within this research as a more practical determination
of crisis type is necessary. Lauras, Truptil and Bénaben (2015) take a different perspective on
crisis categorisation; providing four categories of crises; “by nature, by hazard event, by
speed of action or by intensity” (Lauras et al. 2015: 693). Whilst these categorisations are
clearer than the previously mentioned division, there is still a need for a more concrete form
of categorisation. Therefore, a closer examination of man-made and natural crises is
important.
“Traditionally, the two types of disaster have been (1) natural, i.e. an act of God and
(2) man-made” (Weisæth, Knudsen, and Tønnessen 2002: 34). Man-made crises can be
defined as “the result of a failure of human hand or in human made products” (Weisæth,
Knudsen, and Tønnessen 2002: 34). Park (2011) loosely describes Man-made disasters as
involving “human factors such as poor judgment, poor working condition, poor maintenance
of equipment and/or the negligence of the operators” (Park 2011: 466). From these
definitions man-made crises can be considered as; an event whereby human influence has
caused, or not prevented failure or damage. Contrastingly, Natural disasters are considered as
“unavoidable and to a large extent beyond human control.” (Weisæth, Knudsen, and
Tønnessen 2002: 34). The notion of beyond our control for natural disasters is an important
characteristic of natural disasters (Park 2011). Another definition is supplied by Alexander
(1993) a “rapid, instantaneous or profound impact of the natural environment upon
socio-economic system” (Alexander 1993: 4). The International Federation of Red Cross and Red
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crescent (2017a) societies provides the most practical, clear and concise definition of a
natural disaster; “Natural hazards are naturally occurring physical phenomena caused either
by rapid or slow onset events which can be geophysical, Hydrological, climatological,
meteorological or biological” (IFRC 2017a). As this definition has the most clarity and
conceptual provision, it will be the working definition for this research.
It can be argued that a third form of crises is increasing in prevalence, which is
Technical Failure as a disaster. “Technological hazards arise from various components of
transportation, infrastructure, industry, and building/structures” (Coppola 2007: 32). As
technology increases, adapts and improves the scope and scale of crises involving technology
is likely to increase (Coppola 2007). The International Federation of The Red Cross and Red
Crescent societies links technological and man-made disasters as synonymous, providing the
following characteristics; “complex emergencies/conflicts, Famine, displaced populations,
industrial accidents and transport accidents” (IFRC 2017a). Whilst this pairing by the IFRC
appears logical there is still a distinction between man-made and technological failures with
regards to typing crises. Technological Failures are somewhat preventable in comparison to
Man-made and Natural crises, as protocol and planning should be in place for the prevention
and protection against such events occurring. The United Nations (UN) has a role in
International unity, includes three forms of crises within their rhetoric; natural, Man-made
and technological. Whilst defining a disaster as a
“combination of: the exposure to a hazard; the conditions of vulnerability that are
present; and insufficient capacity or measures to reduce or cope with the potential
negative consequences. Disaster impacts may include loss of life, injury, disease and
other negative effects on human physical, mental and social well-being, together with
damage to property, destruction of assets, loss of services, social and economic
disruption and environmental degradation” (United Nations 2012: 9).
The UN as a leading international organisation, supplies a definition which is applicable to
each country that the cases originate in, as they are all members of the UN. Similar arguments
for these three types of crises (Man-made, Natural and Technical Failure) are mentioned
within other scholarly literature. Therefore, the three main forms of crisis that are most
prevalent in the practical application of crisis management and in crisis management
literature are; Man-made, Natural and Technological Failure. Hence, these forms of crises
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will be the foundation for determining the types of crises which will be used within this
research.
Fractal theory.
For an understanding of fractal theory in the context of crisis management it is
important to understand the origin of fractals. Fractals are a mathematical principle
discovered by Benoit Mandelbrot through his work exploring economic market prediction
and price variation (Mandelbrot 1963). Fractals when defined simply are;
“A never-ending pattern. Fractals are infinitely complex patterns that are self-similar
across different scales. They are created by repeating a simple process over and over
in an ongoing feedback loop … Fractal patterns are extremely familiar, since nature is
full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells,
hurricanes.” (Fractal Foundation 2017).
“Fractals such as the Mandelbrot set are commonly associated with the study of complexity”
(The Economist 2003). Be it in art, finance, science, mathematics or engineering, Fractals are
universally present (The Economist 2003). Fractals are more commonly known through their
use in economics, whereby Mandelbrot noticed similarities between differing price charts and
market fluctuations (Mandelbrot 1997). This understanding of price changes, enabled
Mandelbrot to determine repeating patterns and create a level of knowledge surrounding
predictions for the future financial market. Fixed points within the financial market and the
use of scaling are key features of fractals within the economic sphere (Mandelbrot 1999).
To understand fractals, it is important to first understand the principles upon which
fractals were built. In a generalised form, fractals “bring together under one heading a large
class of objects that have certain structural features in common” (Dyson 1978: 677). Whilst
Mandelbrot does not provide a clear definition of a fractal, there are plenty of characteristics
shown throughout his work. Fractals are “a mathematical set or a concrete object whose form
is extremely irregular and/or fragmented at all scales” (Mandelbrot 1977: 294). Fractals are a
repeating pattern within mathematics which can be “brought usefully to bear not only on
microscopic phenomena but also on phenomena on or above man’s scale” (Mandelbrot 1977:
1). Fractals are also characterised by their statistical nature, of chance and irregularities. The
notion of fractals can be described as shapes which “tend to be scaling, implying that the
degree of their irregularity and/or fragmentation is identical at all scales (Mandelbrot 1983:
1). Fractals in and of themselves comprise of a “simple mathematical feedback loop to
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produce an astonishing variety and complexity of results” (Mandelbrot and Hudson 2010:
145) which can be used to identify repeating patterns within phenomena. Fractals are
constant, repeating patterns that are the same whether they increase or decrease in
scale. “The simplest fractals scale the same way in all directions, hence are called
self-similar” (Mandelbrot and Hudson 2010: 127). This notion of being identical or ‘self-similar’
is not just limited to mathematics and economics; “self-similarity methods are a potent tool in
the study of chance phenomena … very similar considerations apply in the study of
turbulence, where the characteristic sizes of ‘features’ are also widely scattered” (Mandelbrot
1967: 636). In a rudimentary form, self-similarity can be used within differing contexts
whereby repetition at different levels of scale can be perceived and viewed. Mandelbrot and
Hudson (2010) argue that fractals “accurately describes some fundamental principles of how
people often think and behave: in hierarchies, with repetition and scaling” (Mandelbrot and
Hudson 2010: 133). Fractals also use the principle of invariance (Mandelbrot 1983), a
mathematical principle which relies on the idea that nothing has changed, there is no variance
or variety. Invariance revolves around the notion that the element remains unchanged
regardless of the surrounding actions, events and elements. These unchanging elements are
known as invariants.
Topper and Lagadec (2013) supply a new theory, based on identifying invariants in
crisis situations and linked with Mandlebrot’s (1983) notion of fractals. Mandelbrot (1983)
identified repeating identical patterns throughout nature, known as fractals. Topper and
Lagadec (2013) argue that Mandelbrot’s fractal pattern can be applied to crisis situations. The
Fractal theory is impacted by the invariance principle, most commonly used in mathematics
or physics, “Finding an invariant means finding a key to grasping the way the system is
behaving” (Topper and Lagadec 2013: 10). An invariant is something that does not vary and
is self-similar. Looking for what has not changed after a crisis alters the way actions and
responses are determined and can impact the response. “What is invariant from one state to
the other and what can be undertaken to better prepare and manage upcoming crises” Topper
and Lagadec 2013: 11). By “considering what is common in universes where crises happen
on different scales” (Topper and Lagadec 2013: 11) we can determine which action to be
taken are predictable. “The elegance of fractals is also a function of their self-similarity”
(Seeger 2002: 334). By looking at key aspects of crises, invariants become apparent and
patterns identified. In the fractal theory Topper and Lagadec (2013) promote they suggest,
space, time, rank and sense-making as the four dimensions that impact the crisis response
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most. Likewise, different levels of response from local to national will also have a pattern and
a fractal imprint. “Crisis events themselves may also exhibit fractal pattern by repeating
across different organizations and different scales” (Seeger 2002: 334) Once these fractals
have been identified, actions can be implemented to promote improved crisis response
measures. Similarly, the nature of crises has changed from being an isolated event to a
“multifaceted challenging situation mixing hyperlocal and hyperglobal dynamic” (Topper
and Lagadec 2012: 22) which impacts on the response to crisis situations.
A clear understanding of what is a fractal within the context of this research is key,
however it is equally important to understand what is not a fractal. A fractal is: a repeating
action/event/idea/characteristic that is identical and occurs at each level (Local, Regional and
National) to the same degree of occurrence. Therefore, an event/action/pattern is not a fractal
if: the nature or type of event/action/idea/characteristic is not identical. This statement is not
dependant on scale. If the event/action/idea/characteristic occurs at all levels (Local,
Regional, and National) but is not identical or at least self-similar then it is not a fractal.
These guidelines for what is or is not a fractal originate from the Mathematical principle and
standard set out by Mandelbrot (1983).
Crisis Response and levels of response.
The response to crises can be both preventative, corrective or a combination of both
(Lauras, Truptil and Bénaben 2015). The need to be prepared to face any risks or crises works
in tandem with the need to correct and change the response when previous failures do not
give the desired result. The “response to a crisis is linked to the notion of ‘measures taken’”
(Lauras et al. 2015: 697) during the response to a crisis, decisions will have to be put into
effect with the hope of gaining the best outcome, the measures taken will impact the
outcome. Priorities within the response to a crisis can affect the outcome, the most common
goal within “emergency response efforts are to provide shelter and assistance to disaster
victims” (Rawls and Turnquist 2010: 521). Whilst this is an important aspect of crisis
management response, there are other tasks which are key to increasing the success of the
response; “relief, emergency shelter and settlement, emergency health, water and sanitation,
and tracing and restoring family links” (Wex, Schryen, Feuerriegel and Neumann 2014: 698).
The mobilization of resources, such as water, power and medical services and the restoration
of the infrastructure enabling the resources to be mobilized is key (IFRC 2017b).
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Within the context of this research three levels of response will be analysed; Local,
Regional and National. These levels will be used as indicators for determining the actions and
responses taken during the crisis. The Local level can be defined in its most basic
geographical form as “restricted to a particular area or one’s neighbourhood or community”
(Oxford living dictionaries 2017). This definition can then be used to create a working
concept for this research; the local people’s involvement within the epicentre of the crisis
both as responders and victims to the crisis, during and after the crisis event occurs. The
Regional level can be defined as “relating to the regions of a country” (Oxford living
dictionaries 2017). With a working concept of; the regional influence by the authorities and
the people living in that region, which could be a county or state, and their actions taken
during and after the crisis event. The National level can be defined as “Relating to or
characteristic of a nation; common to a whole nation” (Oxford living dictionaries 2017). With
a working concept of; actions taken on a national level to counteract the effects of the crisis,
with directions originating at the head of state and state departments.
Invariants.
Invariants are aspects that do not change. Independent of the surrounding context, an
invariant does not change or adapt; they do not vary.
“the idea behind fractal geometry and its use of ‘invariants’ is, instead of asking
ourselves what is being dislocated, what is falling apart, what is being torn to pieces,
to suggest a new set of questions and a new set of actions to find out what has not
changed, what is invariant from one state to another and what can be undertaken to
better prepare and manage upcoming crises” (Topper and Lagadec 2013: 11).
Within Fractal theory, Topper and Lagadec (2013) supply four aspects of a crisis by which to
measure the similarities and invariants of a crisis; these are Space, Time, Rank and
Sense-making. These aspects are important as this new perspective on crisis management has been
put forward by Topper and Lagadec (2013) and as the theory is relatively new these aspects
are a good starting point for further research. Topper and Lagadec (2013) provide
explanations for all four aspects, however they are extremely vague and do not provide
sufficient detail that is required to effectively observe these aspect within the context of a
crisis. As a result, the concepts have been expanded and influenced using theoretical views
from other authors within the sphere of crisis management.
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The concept of Space is defined as the shift from a localised event to a global event
because of modern day interdependence and movement of people (Topper and Lagadec
2003), mainly referring to geographical space, and often the crisis affects many ‘spaces’ at
the same time. “Modern crises are no longer confined to their site of origin” (Boin and T’Hart
2003: 545). The chain reaction across the globe as crisis events unfold and the response
begins, known as the “Domino effect” (Körnert 2003: 188), changes how crisis events unfold
in terms of geographical spaces. There are “multiple levers of action at the same time”
(Topper and Lagadec 2013). Therefore, the approach to crisis management needs to be both
aware of the events at the epicentre of the crisis but also the far-reaching implications
worldwide. Indicators of space include; the origin of the victims, the origin of the response
workers, the geographical space and the social media impact.
The concept of Rank is defined as the interaction of individuals which impact the
event, through their level of authority and understanding of the situation (Topper and
Lagadec 2003). Rank can impact the response and the chain of command during a crisis.
“Everyone has different information, different perceptions of the same information” (Topper
and Lagadec 2013: 13). Communications and interactions of actors within the response can
impact the outcome and understanding of the situation. Likewise, “preparedness for critical
breakdowns requires rapid and flexible decision-making authority” (Boin and McConnell
2007: 56). This is a complex dynamic which can affect the progression of the crisis response.
The use of authority to dictate action, or overrule another responder’s action or decision
making can also be an aspect of rank. The indicators of rank that will be analysed include; the
type of responders present at the event, the level of authority of the individuals in charge, the
level of respect/priority the victims and fatalities held, the communication between victims
and responders.
The concept of Sense-making is explained as the sharing of information and
understanding about the situation. Differing individuals may have a different view on the
situation causing further complications in sense-making of the event. “Sense-making is,
importantly, an issue of language, talk, and communication. Situations, organizations, and
environments are talked into existence” (Weick, Sutcliffe and Obstfeld 2005: 409). As
events, actions and ideas are socially constructed, the influences behind decision making
affects the outcome (Weick et al. 2005). “A collective understanding of the nature,
characteristics, consequences and potential scope and effect of an evolving threat” (Boin,
Kuipers and Overdijk 2013: 82) is extremely important, especially when large numbers of
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personnel are involved. Sense-making of the actions by individuals during a time of crisis is
to “render the subjective [crisis] into something more tangible” (Weick 1995: 14). The
indicators of sense-making include; actions and opinions of responders, authority and who
gives the directions during the event, the individuals whose ideas and opinions are listened to
during the event.
The concept of Time encompasses the “short term event to the long-term impacts”
(Topper and Lagadec 2013: 12). Both instant and long-term dynamics impact the response
process, from immediate reactions on social media to the clean-up process towards the end of
the event. The time frame in which actions occur in the immediate aftermath can work to
prevent the loss of life, but also when actions are not organised or planned for, further
damage can occur. Crisis management in general focuses on the short-term impacts of the
initial crisis event however long-term issues also need to be resolved as society returns to
normality (Van Wart and Kapucu 2011). Both instantaneous consequences and long-term
consequences overlap during a crisis response. The crisis event “is not limited to a single
timeline approach … overlapping timelines that have different dynamics and fundamental
building blocks” (Topper and Lagadec 2013: 13). Actions in time are identified through the
responses of the emergency services, victims and citizens. Time constraints and actions in
time can affect the resources available and how emergency services respond in a time of
crisis (Van Wart and Kapucu 2011). Indicators of the actions in Time include; the responders,
the victims, the physical time and the aspects of the event themselves; response time to the
initial event, social media response, government announcements and reactions, emergency
services and clean up time.
All four of these concepts within Fractal theory need to be operationalised to become
understandable in the context of case study analysis. The operationalised definitions of Space,
Time, Rank and Sense-making are summarised below.
Space: The environments affected by the event, in which fatalities, victims and
responders interact. The locations in which interactions take place during and after the event
which impact the response and outcome of the event. The understanding of the progression of
events from the epicentre spreading worldwide through media and communication.
Rank: The use of authority in making decisions, leading actions and attitude taken
with other responders and victims. The actions and event are interpreted by responders in
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their actions to authority and victims of the event. The use of authority to dictate action, or
overrule another responder’s action or decision making can also be an aspect of rank.
Sense-making: The opinions and actions of individuals, both victims and responders,
and how this impacts the actions taken. The use of language during the response and how
interactions take place in relation to the crisis.
Time: The time scale by which aspects of the crisis occur, between the initial event
and the concluding clean-up of the event. The actions in time can be separated into action of
the responders, actions of the victims, the moments of the events within the crisis and the
physical timeframe of the crisis. Also included is the physical time it takes for the response to
occur at all level of service response. This includes the time taken for news of the event to
spread across the globe through social media and communication between witnesses, victims
and families. Time includes the physical time events and time between components of the
crisis response, how time impacts the victims, responders and when aspects of the crisis
occur.
Whilst all these aspects of fractal theory are important, only Time will be researched
further. This is to increase the feasibility within the time frame permitted for this research,
whilst also including the necessary aspects provided within Topper and Lagadec’s (2013)
theory framework, enabling a more structured and accurate examination of time within crisis
management. Time is the most effectively identified within the reports and will yield a
respectable level of results that can be analysed enabling a more valid and reliable result.
Methodology.
The objective of this research is to determine whether Topper and Lagadec’s (2003)
theory on fractal crises is applicable to real cases and determine whether looking at the
normal rather than the abnormal can impact crisis management. This will be a comparative
case study analysis, enabling Fractal theory to be implemented in differing types of crisis to
determine whether it remains effective and applicable. A comparative case study is being
used as it enables specific aspects of a crisis to be examined in detail, whilst also allowing for
comparison between cases. “It [Comparative case studies] sharpens our power of description,
and plays a central role in concept-formation by bringing into focus suggestive similarities
and contrasts among cases” (Collier 1993: 105). This understanding of comparative research
highlights the advantages of using this method to compare crises and the applicability of
fractal theory when looking at time invariants. As this is an explorative study, it aims to be
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the first indication for the application of fractals within crisis management and crisis
response. It will indicate whether being the first application of fractal theory is considered a
desirable trait for research. As the research is explorative, the results will not be perfect but
will provide a new and deeper understanding of fractals within crises. Whilst this research is
new and potentially opens new, exciting ways of dealing with crisis management and crisis
response, it is important to understand that “Exploratory research rarely yields definitive
results.” (Neuman 2014: 38). However, the research will aim to open up the field of research
into a more detailed study of fractals within crisis response.
The time aspects of each case will be analysed at each response level; Local, Regional
and National. This will then be compared to the other cases and will enable a distinction to be
determined regarding the Time invariant of crises according to Fractal theory (Topper and
Lagadec 2003). The research will be conducted using qualitative methods within the context
of a case study. The hypothesis of this research is; Time invariants will be observable as
a fractal within all types of crisis.
The advantages of using case study analysis are numerous. Case studies provide a
heuristic impact (Neuman 2014) enabling further learning and discovery for pushing
boundaries and new theories. Which, as Fractal theory is relatively new, is extremely
appropriate for this form of research. Case studies have the “ability to capture complexity
and trace processes” (Neuman 2014: 42). Case studies enable the researcher to look at the
bigger picture whilst also focusing in on key elements. Case studies within this research will
allow for the complex nature of crises to be clearly organised, structured and provide a deeper
understanding of the events and circumstances within each case. Similarly, case study
analysis allows for a deep dissection of the crisis enabling an increased understanding of the
results and a more valid and reliable way of tackling a difficult subject. Case studies allow for
multiple cases to be compared, which allow for any potential generalisation surrounding
fractal theory, time invariants and crises. The use of case studies is also reflective of the data
sources that will be used. As the data is from evaluation reports about the crises, using a
qualitative research method fits with the data. Using case studies allows for in depth analysis
of events that happened in the past. Similarly, it allows for a wide variety of cases to be
analysed and compared, creating a bigger picture of the real, practical crisis response process.
There are disadvantages to using case study analysis which need to be addressed.
Conducting case study analysis may be considered not rigorous enough if a systematic
procedure has not been followed (Yin 2013). This disadvantage will be overcome with the
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use of a clear process for analysing the data. Generalisation of the findings whilst preventing
subjectivity from impacting the results is challenging.
This research uses case study analysis as it allows many different types of crises to be
scrutinised against Fractal theory, whilst also looking to identify patterns that occur in a
practical form within crisis management. The practical nature of crisis response requires the
use of a form of research method that can be applied in the real world.
The data sources used will be the government reports, commissions, recommendations, and
plans and protocols pertaining to each crisis. Specifically, evaluation reports of the crisis
response for each crisis will be used, as they provide an independent, unbiased perspective of
the crisis response, increasing validity and reliability. These documents have been chosen as
they are clear, and explicit accounts of the event with information regarding the response at
all levels (Local, Regional, and National) and over the time frames of the events including
before, during and after. They are high quality documents that are accessible to the public,
and produced by governments, governing bodies or accredited associations. The reputation of
these bodies increases the validity and reliability of the sources and hence the research.
Unit of Analysis The Crises – crisis response actions at each level, specifically related to Time.
For example, the actions of the Police will be analysed at all levels, Local, Regional and National, with Time invariants being isolated. Unit of observation The reports provided post-crisis.
For example, the 9/11 Commissioners report.
Observation The Time invariants at all levels: Local, Regional, and National For examples, when evacuation of citizens/residents occurs.
Score The invariants that remain the same during all types of crises and at each level of response during each type of crises.
Table 1 Elements of analysis
Case selection.
Below are the cases that have been selected to represent each type of crisis (See Table 2).
Only three of each type of crisis has been selected due to the limited time scale for this
research. As this research is exploring the potential of Fractal theory, this number of cases
will give a sufficient indication of the applicably of the theory. Each case should offer a
different form of each type (Man-made, Natural and Technical Failure) to have a varied and
wide range of cases, increasing the validity of the results. This also allows for the potential to
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get an understanding of the generalisation associated with Fractal theory, Time invariants and
crises. Each type of crisis should be represented through the three cases selected for each
type, with respect to the accessibility of reports and data sources. Each case has an
availability of evaluation reports that are used within this research (See Figure 6).
Collectively, these cases were selected as they offer a variety of events and the necessary
documentation and reports were accessible. However, there are also specific reasons as to
why each case was selected to represent the type of crisis they are being used for.
Man-Made Natural Technological Failure
Case 1
9/11 Terror attack 2001 (United States of America)
Case 4
Hurricane Sandy 2012 (United States of America)
Case 7
Flight 1549 Hudson River crash 2009
(United States of America) Case 2 7/7 Bombings 2005 (London) Case 5 Sheffield Floods 2007 (London) Case 8
Hatfield Rail Crash 2000 (London)
Case 3
Costa Concordia Shipwreck 2012 (Italy) Case 6 Christchurch Earthquake 2010-2011 (New Zealand) Case 9
Fukushima Nuclear Plant 2011 (Japan)
Table 2 Cases to be analysed
These cases were selected for a variety of reasons, which will now be individually discussed.
Case 1 – Man-made – Terror Attack - 9/11. This case was selected as the crisis was deemed a
changing point in the war on terror. The location of the World trade centre towers, being in
such a high-density area, made for a challenging crisis response. The locations over multiple
states demanded a variety of responses.
Case 2 – Man-made – Terror Attack - 7/7. This case was selected as there were difficulties
with the locations of the bombs. Three bombs were on three different underground trains and
one was on a bus in a different part of London. Communication issues and slow emergency
responses were key aspects in the response to this crisis. This crisis is like 9/11 in that they
are both terror attacks, however this one is different as the locations were scattered around the
city and all individual victims involved have been identified and the search officially
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ongoing, with individuals still missing. The Bombs on the underground trains were exploded
simultaneously, whereas on 9/11 the planes that crashed into the buildings were not at the
same time, but spread across the morning of 9/11.
Case 3 – Man-made – Human Decision Making - Costa Concordia. This case was selected as
human failure and decision making caused the event. The intent to cause harm was not part of
the captain’s decision, which differs from 9/11 and 7/7 where the intent to harm was an
integral aspect of the crises. Also, as the event occurred on a boat in the sea, the dynamics
surrounding response is different to both 9/11 and 7/7. The location of the event, off shore
from the Italian coast, also allows for a developed country providing the response and
evaluation of the response which fits with all the other cases that will be analysed.
Case 4 – Natural – Hurricane - Hurricane Sandy. This case was selected as the hurricane
affected many states, with the worst hit being New York. The determination of the
emergency services, the city residents and businesses to reopen the city post crisis, affected
the crisis response. It is also interesting to analyse the response in relation to 9/11 and
potentially compare the response, as the same city was affected but 11 years apart and both
crisis type are different.
Case 5 – Natural – Flood - Sheffield Floods. This case was selected as the flooding was not
due to any other natural weather event, but is purely because of large volumes of rain fall.
The case is also considerably smaller than both the other natural crises, enabling a better
overall representation of natural crises analysed in this research. This will increase the
validity of the generalisation that will be made about natural crises as different sizes of crises
have been analysed.
Case 6 – Natural – Earthquake – Christchurch Earthquake. This case was selected as an
earthquake of this magnitude and devastation in a developed country has not previously
occurred to this scale. Also, the area that was struck by the earthquake has been declared no
longer hospitable and the local council has relocated, with most residents moving elsewhere
in New Zealand, even to Australia. The change in location of the council potentially affected
the response as the area was deemed unsalvageable due to future potential earthquakes.
Case 7 – Technical Failure – Engine Failure - Flight 1549. This case is interesting due to the
plane landing in the river, making accessibility difficult and challenging for first responders.
The plane landing on the water adds a different element for the response teams to tackle. This
crisis response was also marginally prepared as the pilot was able to give warning to air
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traffic control, enabling an alarm to be sent. This affects the response speed and planning
surrounding the approach to the aircraft and how best to deal with the passengers and crew on
the plane.
Case 8 – Technical Failure – Rail Fault - Hatfield Rail Crash. This case was selected as there
is no question that the crisis was a technical failure. The drivers were cleared of any
responsibility, with faults and a crack being discovered in the rails the train was traveling
over. The drivers followed correct protocol and proceeded with following on the protocol for
such an event. This case is also small in comparison to Flight 1549 and Fukushima as the
location was limited, and the victims were those on board the train with no external personnel
injured or adversely affected.
Case 9 – Technical Failure – Reactors unable to function - Fukushima Nuclear Plant. This
case was selected as the health implications of this crisis make it interesting. Nuclear power
and the dangerous side effects are known but little protection protocol was in place,
increasing the damage caused by the crisis. The danger of radioactive leaks and nuclear
power stations are known, however minimal protocols were in place to protect workers and
residents. There were no protocols for wider impact of such a disaster. Also, this crisis
occurred in Asia, providing a different cultural aspect to the response. The implications of
differing culture to the other cases my affect the outcome of the response.
Time – conceptualised.
Actions in Time will be analysed as this provides a range of events and actions that
responders act upon. Actions in Time has been selected instead of actual moments in time. As
moments in time are difficult to determine through reports without physically seeing the
event and it is difficult to maintain meticulous recordings for every minute. Not all the reports
contain such detailed recordings and therefore comparisons between cases would not be
appropriate, reliable or valid. Within the Invariant of time, four subsections will be used to
clearly conceptualise and identify the time fractals in the crisis event; specifically, those
relating to actions in time. These are: the event itself, the numerical/physical timeline, the
actions of the responders and the actions of the victims. Whilst there will be some overlap
between the subcategories, ever effort will be made to clearly define the subcategory the data
fits into. These four subcategories have been selected as they cover a wide base of actions in
time within crisis management and are relatively simple to identify and isolate within the
context of documents and reports.
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The event itself relates to the factors beyond the control of the responders and victims,
the factors that elicit a response from either victims or responders. This subcategory will be
adaptable depending on the type of crisis, a Man-made crisis will have different aspects than
a Natural or Technical Failure crisis. For example: aftershocks of an earthquake, fires
continuing after the initial event, technology failing and creating a chain event of failure to
other locations etc.
The numerical/physical timeline is the chronological structure of the event, a clinical
linear line of the events. For example: exact references to time, at 9.00am the police arrived.
The time difference between the event and the arrival of services etc.
The action of the responder relates to when any action or decision is made by
responders, be it immediate search and rescue or government policy. For example: when the
emergency services decide to withdraw from the scene of the crisis, when shelter and
temporary housing becomes available etc.
The subcategory of actions of the victims relates to when the victim acts and reacts to
the event and the support they are provided with post-crisis. For example: calling the
emergency services, helping with the clean-up of debris, decision to evacuate etc.
Concept Topper and Lagadec’s (2013) Definition
Concept operationalised. The physical time parameters for
each crisis
Time The time from “short term event to long term impacts” (Topper and Lagadec 2013: 12)
The time scale by which aspects of the crisis occur, between the initial event and the concluding clean-up of the event. Also included is the physical time it takes for the response to occur at all level of service response. This also includes the four subcategories of time; the event itself, the Physical timeline, the actions of the responders, and the actions of the victims (See Figure 4).
The research will include anything from the moment at which the crisis occurs, for example when the Bombs exploded on the London underground. Up Until the point at which the reports stop detailing the event, for example when the commission determines that the response to the event is over.
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Operationalization.
Figure 4 Diagram of the operationalisation of Time
The case study approach that will be used aims to analyse each case individually and
then compare the cases to determine the universality of fractal theory amongst the cases,
using a deductive approach. Answering the question: To what extent do different types of
crises, individually and collectively, demonstrate Topper and Lagadec’s (2013) Fractal
theory, specifically with reference to the concept of Time?
Each case will be analysed for the Time invariants and fractal patterns. The Time
invariants once isolated will be examined and analysed at three levels of response; Local,
Regional and National. A generalised picture of Time invariants at each level will be
composed and a detailed analysis of each aspect will be completed using data gathering and
information from the official crisis reports. This will increase ease and availability for the
creation of generalisations and comparisons which can be used to determine an overview for
answering the research question. The research will be conducted using open systematic
coding. The parameters for the coding that will be used originate in the operationalised
definitions of actions in Time. Every isolated function of time within the documents relating
to the Time invariants at any of the three levels; Local, Regional and National, will be
analysed to create a bigger picture of the situation. If there are any discontinuities within the
documents that are not covered by the parameters set above or keywords below, they will be
isolated and then judged on their relevance in helping or hindering the research. As the Time
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