Chaos Theory

A model subglacial drainage system, coupled to an ice-dammed reservoir that receives a time-varying meltwater input, is described and analysed. In numerical experiments an ice-marginal lake drains through a subglacial channel, producing periodic floods, and fills with meltwater at a rate
dependent on air temperature, which varies seasonally with a peak value of Tm. The analysis reveals regions of Tm parameter space corresponding to ‘mode locking’, where flood repeat time is independent of Tm; resonance, where decreasing Tm counter-intuitively increases flood size; and chaotic dynamics,
where flood cycles are sensitive to initial conditions, never repeat and exhibit phase-space mixing. Bifurcations associated with abrupt changes in flood size and timing within the year separate these regions. This is the first time these complex dynamics have been displayed by a glaciohydraulic model
and these findings have implications for our understanding of ice-marginal lakes, moulins and subglacial lakes.

Özet
Matematiğin mimarlık dahil olmak üzere farklı disiplinlerle girdiği sıkı ilişki ve teknolojinin gün geçtikçe gelişmesiyle kullanım alanı artan bilgisayar destekli tasarım teknolojisi sayesinde tasarım sürecinde farklı matematiksel modellerin kullanılması mümkün olmuştur. Matematiksel modellerle strüktür tasarımı, geometri ve malzeme parametrelerini ön plana çıkarmıştır. 
Karmaşıklık kuramının sistemdeki dinamiklerin modellenmesi açısından strüktür tasarımındaki rolü önemlidir. Birbirinden farklı birçok parametrenin olması ve bunlar arasındaki ilişkilerin keşif süreci taşıyıcı sistemi tasarlanabilir bir sistem yapmıştır.  Geometri, bu sistemin formunu oluşturur ve ilk dikkat çeken parametredir. Yaratılan her form bir geometri içerir ve formun ayakta durabilmesi için de strüktür tasarımına ihtiyaç vardır. Mimarlıkta geometriyle birlikte malzeme, tasarımın dokusunun, biçiminin ve binanın görünümünün oluşmasında temel bileşenlerdendir.
Strüktür tasarımında en temel yöntem olan sonlu elemanlar analizi ışığında, arup optimizeri, dinamik rahatlama, evrimsel şekil optimizeri ve evrimsel strüktür optimizeri incelenmiştir. Bu analizler sonucu ortaya çıkan zincir eğrisi, bükülme, minimal yüzey ve nurbs modelleri araştırılmıştır. Arup optimizeri, tüm sistemde kendi kendini organize etmesini sağlayacak en uygun tekrar elemanlarını seçer ve bu elemanları tek tek analiz eder. Dinamik rahatlama, malzemenin yerçekimi ile kendiliğinden şekil almasını sağlayan topolojik şekildeki kemer yapının optimizasyonunu sağlar. Evrimsel şekil optimizeri ise serbest forma en uygun alanı seçmek için en az deplasman yaptıracak strüktürel eleman yerleşmesini analiz eder. Evrimsel strüktür optimizeri ise sistemde vektörel gerilimi azaltmaya yönelik analizler yapar.
Strüktür modellerinden zincir eğrisi modelinde zincir, yerçekimine karşı oluşan eğrinin formunu alır. Bükülme, malzemenin kırılma noktasının gelişen teknoloji ve yeni malzemelerle eşik değerinin artması sonucunda, eski kırılma noktasının bükülmesiyle oluşan formdur. Minimal yüzeyler, minimum yüzey-gerilim potansiyel enerjisine sahip ve alan olarak da minimum olan formlardır. Nurbs ise üniform olmayan çizgiler eğrisidir ve bu eğriler, bir strüktür modelinde geometrinin haritalamasını yaparak serbest form yapıların strüktüre referans olabilecek olası çizgi ve yüzey ilşikilerinin hesaplanmasında kullanılırlar.
Matematiğin bir model oluşturduğu bu strüktür sistemlerinde, bilgisayar ortamında oluşan simülasyon, geçmişin sıkıcı ve anlaması zor olan hesaplamalarını geride bırakıp mimar ve mühendislere ortak olarak kullanabilecekleri bir ara yüz oluşturmuştur.

          Anahtar Kelimeler: Strüktür Tasarımı, Karmaşıklık Kuramı, Optimizasyon, Geometri, Kendi kendini Organize Etme, Topoloji

Chaos je tradiční protiklad řádu: oblast nerozlišitelnosti, neartikulovatelného zmatku a nepředvídatelných vpádů. Původní řecké slovo evokovalo rozevřený chřtán, do něhož může být vše řádné, leč neopatrné vtaženo. Chaos nicméně nezůstal v průběhu času čistě negativním pólem – kdo v sobě nemá zárodečný chaos, nezrodí tančící hvězdu, napsal Friedrich Nietzsche, znalec antické kultury, a skutečně v mnoha kosmogonických mýtech najdeme chaos na počátku jako původní živel a podmínku vzniku světa, smysluplného celku, kterým proniká přirozené světlo rozumu. Potřebujeme a chceme řád: chceme, aby vlaky a tramvaje jezdily podle jízdního řádu, aby nás lidé ve frontách nepředbíhali, potřebujeme kontinuitu, integritu a předvídatelnost. A zároveň potřebujeme chaos, náhodná setkání, která jsou podmínkou myšlení a základem jakékoliv zábavy, potřebujeme překvapení. Ve skutečnosti se obyvatelná skutečnost nachází někde mezi, na hranicích chaosu a řádu, na hranicích, které mají s největší pravděpodobností fraktální strukturu. XXX V průběhu 20. století došlo k něčemu, co bychom mohli nazvat rehabilitací chaosu. Nestalo se tak úplně náhle a nepředvídatelně, ale mělo to, jak je v blízkosti chaosu obvyklé, nenápadné počátky a výrazné následky. Pro pojmenování malé změny počátečních podmínek vedoucí k ohromné změně ve výsledku se vžil pojem motýlí efekt, který souvisí se známou představou motýla, jenž mávne křídly nad Brazílií a způsobí tornádo v Texasu – dnes slavný teoretik chaosu Edward Lorenz použil tento motiv v názvu své přednášky z roku 1972, ale jeho původ lze vysledovat třeba až k filosofu Johannu Gottliebu Fichtemu (" Nelze pohnout zrnkem písku, aniž by se nezměnil celý nesmírný celek. ") či k Rayi Bradburymu a jeho povídce Burácení hromu z roku 1952. Lorenz byl meteorolog a na to, jak velkou měrou přispěl k definování teorie chaosu, se přišlo poměrně pozdě. Jak píše James Gleick v knize Chaos, nikoho z těch, kteří se na počátku šedesátých let chaosem zabývali, nenapadlo hledat inspiraci na stránce 130 ve 20. svazku meteorologického věstníku. Chaos či přesněji studium deterministického chaosu se v dalších letech stalo velmi populárním tématem. Ukázalo se, že tento typ popisu dokáže úspěšně mapovat chování složitých systémů, jako jsou počasí, burza nebo město, tedy vše, co je dostatečně složité, aby se organizovalo samo. Můžeme celkem bez obav tvrdit, že na počátku všeho nového je zapotřebí období chaosu, v němž se rozpustí staré struktury a vrstvy a vykrystalizují nové. V případě teorie deterministického chaosu však šlo o zkoumání samotného chaosu a jeho vlastností, což umožnily až nové nástroje, především výpočetní technologie, které změnily způsoby zkoumání dynamiky složitých procesů. Klíčovými pojmy jsou tu simulace, iterace a vizualizace.

This study examines that in what aspects the levels of leaders' emotional intelligence in chaos and complexity situations can affect the organizations. Also, in this study the dimensions of emotional intelligence which are closely related to social life and organizational systems will be considered in terms of chaos and complexity theories. At the same time in this study, how a situation that appears to be complex but has an order inside and has the potential to be directed with small interventions can be handled by a leader that has a high capacity of using his/her emotional intelligence will be scrutinised. Additionally, this study will present the advantages of some leader capabilities (such as personal and interpersonal relationships, stress management, adaptability, general mood, empathy, motivation and self-awareness) in the management of the organizations in the context of chaos and complexity theories. Last but not least, the effect of emotional intelligence level in the...

The Positive Disintegration (Dabrowski, 1996) is the process of transition from the point attractor (primitive integration) to the cycle attractor (unilevel disintegration) and then to the chaotic attractor (spontaneous multilevel disintegration) and an emerging order (organized multilevel disintegration) and an order (secondary integration) with increasing complexity. A driving force for this development is the movement from simplicity toward complexity. Mental structure is maximizing its complexity and therefore its stability by pushing forward to higher levels.
We analyze in details the spontaneous multilevel disintegration described by the chaotic attractor. The spontaneous multilevel disintegration corresponds to the period of adolescence. As an individual makes transitions from childhood to adulthood, from dependence to independence, the changes in behavior are dramatic. As soon as person feels that some modes of thinking, feeling, and acting are higher, conflicts of a vertical nature arise. Emotional, unconscious and slightly conscious forces dominate the spontaneous multilevel disintegration.
We show that the process of spontaneous multilevel disintegration corresponds to dramatic changes in brain of adolescent. During adolescence, brain organization and function enter a unique period of change. The emotional behavior of adolescent is due to increased reliance on the instinctual part of brain (amygdala) while the area of rational thought, the frontal lobes develops. We postulate that the positive maladjustment appears when the brain activity of teenager seems to shift from amygdala to frontal lobes and emotions becomes more conscious and selective.

أحيانا تتسم محاولة الاقتراب من حالة عدم اليقين بقدر كبير من الصعوبة، وأحيانا لا يتم التعامل معها بجدية، وكلنا نذكر مقولة رامسفيلد والتي عبر فيها عن مستويات مختلفة من حالة عدم اليقين،  حين علق على التقارير التي تنفي وجود أدلة على دعم العراق للمنظمات الإرهابية. وقد أثار حديثه عن وجود أشياء نعرفها وأخرى لا نعرفها العديد من ردود الفعل العالمية. وإدراك رامسفيلد لهذه الحالة، حين كن وزيرا للدفاع، يعني من الناحية العملية، أن القادة العسكريين لا يستبعدون فكرة وجود أشياء لا يعرفونها،  وبالتالي يكون السؤال المنطقي كيف سيتعاملون معها؟.

يحاول هذا القسم من الملحق الاقتراب من حالة عدم اليقين، من خلال تعريف هذه الحالة والفرق بينها وبين المخاطرة، وبينها وبين الفوضى، والأسباب التي تتسبب في نشأة هذه الحالة، ومستوياتها المختلفة، ومدى اهتمام أدبيات العلاقات الدولية بها وبتفسيرها.

كما يناقش المداخل النظرية التي يمكن من خلالها فهم حالة عدم اليقين والتعامل معها، مثل نظرية النظم الديناميكية المعقدة، ومفهوم البجعة السوداء، ونظرية المباريات، ونظرية الاحتمالات. كما يناقش مجموعة من المفاهيم التحليلية والنظريات المرتبطة بحالة عدم اليقين، مثل نموذج السير العشوائي، والتفكير خارج الصندوق، ونموذج "كومة الرمل"، وفكرة "الأجسام الثلاثة"، والفوضى الخلاقة، ولعبة الدجاجة، ومعضلة السجينين.

The Butterfly Effect is commonly known as the thoroughly entertaining idea that a butterfly flapping its wings somewhere in the Amazon valley could cause a tornado in Texas. The idea goes back half a century ago when an MIT meteorology professor named Edward Lorenz made an amazing discovery. In this article I attempt to separate fact from fiction and to determine the scientific importance of this phenomenon, if it really exists.

Security and secrecy are some of the significant concerns in the communications world. In the last years, several encryption techniques had been proposed to improve the secrecy of the information transition. Chaos-based encryption techniques are being exceedingly studied as part of the because of the random-look nature and very unpredictable of the chaotic signals. In this study, a digital-based mobile communication system was proposed that uses chaotic encryption code, Arduino platforms was utilized for this work because it possess an open-source prototyping platform, software and hardware very accessible and extremely flexible to be customized and extended. The ASCII code of input message signal was encrypted using a Chaotic Random Number Generator it will send to the receiver side through mobile GSM system. In the receiver side, the ASCII coded message was decrypted using the same Chaotic Random Number Generator code for decryption. The target of this system is to make a more sec...

Organizations in the 21 st century deal with constant changes such as globalization, technological evolutions, regulatory changes, competition, and other unexpected events, among others. These challenges can be viewed and addressed through the lenses of contemporary theories. This paper selected three contemporary theories namely chaos, complexity, and contingency theories, and presented their foundations and characteristics by comparing and contrasting their key concepts. These concepts include nonlinearity, feedback, bifurcation, strange attractors, fractals, and self-organization for chaos theory; nonlinearity, dynamism, feedback, self-organization, emergence, and adaptability for complexity theory; and adaptation, equifinality, effectiveness, and congruency for contingency theory. Examples of studies and organizational applications of these theories were provided, and implications for scholars and organizational leaders were discussed. By explaining notions such as how the capacity of a system could be greater than the sum of the capacities of its subunits, this paper can act as a starting point for anyone seeking to understand the three theories or use them for research or organizational purposes.

The thesis is on urban interventions, highlighting how void and unbuilt spaces carry as much importance as build spaces.
That architecture is not only confined to built structure, an open void with small interventions causing butterfly effects are as important.

It can be said a) that the world of democratic outcomes(DO) is the world where the
democratic process(V1) bring together competing group of individuals in order to
determine who rules in that democracy; and b) that without clear participation and voting rules, the resulting democratic outcome(DO) can be a normal democratic outcome(NDO) where the majority view rules or an extreme democratic outcome(EDO) where the minority view rules depending on whether the will of the majority(T) or the will of the minority(M) is reflected by the group who wins the democratic process(V1). In other words, if there are no clear rules governing participation and winners and losers in a democracy anything can happen.
It can be said that the world of normal democratic outcomes(NDO) is the world
where the majority view(T) wins the majority rule based voting contest(V = TM ) one
person one vote as everybody is expected to participate and vote. In other words, this
world operates under no complacency(NC) or no protest behavior. Here, there are clear rules governing winners and losers as well as there are clear participation expectations: the true majority(T) wins under no complacency(NC) and the true minority(M) loses as all members vote for the candidate of their preferred choice. And therefore, in true democracies under majority rule the following holds true: V1 = V = TM, where T wins. If we look at extreme democratic outcomes(EDO) as the total opposite of normal democratic outcomes(NDO), then it can be said that the world of extreme democratic outcomes(EDO) is the world where the true minority view(M) wins the majority rule based voting contest(V) one person one vote in a true democracy and where the view of the true majority(T) loses as the democratic process in this case is operating under some kind of minority rule friendly complacency behavior(C = ?). In other words, extreme democratic outcomes(EDO) take place when democratic systems are under some time of extreme  democratic outcome friendly complacency(C = ?) or protest behavior. This is true because the opposite of no complacency(NC) is complacency(C) so extreme democratic outcomes(EDO) can be seen as normal democratic outcomes(NDO) when upside down, but they require a special type of complacency(C = ?) to take place and to persist, a minority rule friendly one. And notice that if we know the specific type of minority rule friendly
complacency(C = ? = C*) that leads to extreme democratic outcomes(EDO) then we can device ideas on how to reverse them totally or partially or we can see ideas on how to avoid them all together. As you may know, in 2017 the UK decided to seek a wider mandate for BREXIT and the BREXIT side lost the referendum, a result that signaled a weaker mandate reversing the EDO tendency partially; and notice that democracies that were supposed to go extreme in 2017, the Netherlands, France, Germany, and so on stayed within the normal democratic outcome(NDO) world, and the question in all those cases is why that was the case?.  Therefore, the sudden coming of extreme democratic outcomes(EDO) in 2016 such as BREXIT and USEXIT raised important questions relevant to understanding the behavior of the majority rule based democracy when upside down. Among the relevant questions raised are the following: a) What type of complacency(C = ?) leads to extreme democratic outcomes(EDO)?; b) What is the structure of BREXIT and USEXIT in terms of this specific type of complacency?; and c) What can be done to reverse and also what
can be done to avoid extreme democratic outcomes(EDO)?.  Among the goals of this paper is to provide an answer to these questions both graphically and analytically using qualitative comparative means.

Given the complexities of our time, it is not surprising that criminological models, theories and perspectives often fall short of providing complete and satisfactory explanations of complex phenomena.  Organised crime and terrorism, and the emerging crime-terror nexus, are examples of such phenomena.  If they were simple, they would be easy to understand and prevent, but they are not.  Complexity science (‘complexity’) studies complex phenomena.  Given the nature of organised crime, terrorism and the crime-terror nexus, one would expect that the family of complexity, including chaos theory, might lend itself to furthering our understanding and knowledge of these phenomena.  Drawing on the natural and social sciences, this thesis explores the notion.  In doing so, a new complexity model, using borrowed science, is developed to apply complexity in a criminological context, and to critically examine organised crime, terrorism and the crime-terror nexus through a complexity lens.  The new complexity model is tested using the case study method and considers whether the new model furthers our understanding and knowledge of these complex phenomena, together with practical and policy implications.  The thesis also considers whether the new complexity model adds a new tool to the criminologist’s toolbox to provide fresh and novel insights into complex problems.

Le recours contemporain à la notion de "complexité" renvoie fréquemment à des démarches ayant tendance à unifier sa définition. En langue anglaise, sa réduction à une forme singulière (complexity theory ou complexity science) s'avère ainsi susceptible de masquer la variété des théories permettant de rendre compte des implications inhérentes au recours à cette notion. Cet article, en prenant en considération à la fois les traditions de recherche latines et anglosaxonnes, associées à la notion de complexité, suggère une approche plus nuancée, évitant la simplification de cette notion à certaines des conceptions dominantes qui y sont associées. Partant d'une approche étymologique, cet article propose d'envisager de façon chronologique l'émergence de trois générations de théories de la complexité; ce faisant, certains de leurs enracinements épistémologiques et socio-culturels sont introduits. D'un point de vue épistémologique, la réflexion proposée met en évidence certaines des interprétations hétérogènes sous-jacentes à la définition de ce qui est perçu comme complexe. Suivant une perspective anthropologique, ce texte évoque également la portée à la fois émancipatrice et asservissante susceptible d'être associée à l'idée de complexité. Sur la base des ambiguitiés mises en évidence, cet article suggère finalement de concevoir les contributions renvoyant aux théories contemporaines de la complexité, au même titre que la remise en question de leur légitimité épistémologique et éthique, à partir des boucles et des dynamiques dont elles sont constitutives. Ce faisant, les chercheurs et les praticiens en Sciences de l'éducation devraient considérer leurs pratiques en tant que processus
d'apprentissage dont la complexité renvoie autant aux transformations qu'ils étudient ou provoquent, qu'aux transformations inhérentes aux systèmes de représentations
auxquels ils ont recours pour les conceptualiser.

Arthouse Tacheles, Kyoto School and Chaos Theory ...

Presented at the conference Indeterminate Futures / The Future of Indeterminacy, University of Dundee (UK), 13 – 15 November 2020; published 2 November 2021: https://queenmobs.com/2021/11/how-long-is-now/

The future is no longer seen as open. But before aligning ourselves to the mantra of the “slow cancellation of the future” (Mark Fisher) we should firstly have a closer look at the present, now: for if we can show that the present is indeterminate, it will be a simple task to show that the future is indeterminate as well.

The now is both a particular now – our contemporary present – and each now throughout history: the present now is thus unique. Unlike the future and the past, the now may not be reduced to statistics, probability or algorithms: according to a Sufi’s saying it is the sword that cuts time into two. To counter the “slow cancellation of the future” we thus must become aware that the doctrine of determinism merely holds for the past. Our political and artistic practice may be wholly unpredictable if we literally engage with autopoiesis, dynamic systems and feedback loops right at the edge of chaos, thus transferring an originally scientific concept to politics and arts. If understood precisely, the now is able to disrupt the pattern of determinacy through the unpredictable event of chaos. If the present now is open, the future is open too.