Chaos Theory: A Brief Introduction. What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data. When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. Figure 1: Lorenz's experiment: the difference between the starting values of these curves is only .000127. When he came back an hour later, the sequence had evolved differently.
By all conventional ideas of the time, it should have worked. This effect came to be known as the butterfly effect. The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Explainer: what are fractals? Fractals are exquisite structures produced by nature, hiding in plain sight all around us.
They are tricky to define precisely, though most are linked by a set of four common fractal features: infinite intricacy, zoom symmetry, complexity from simplicity and fractional dimensions – all of which will be explained below. The next fern you encounter will provide a great illustration of these features if you pause for a closer look. First, notice that the shape of the fern is intricately detailed. Remarkably, you can see that the leaves are shaped like little copies of the branches. In fact, the entire fern is mostly built up from the same basic shape repeated over and over again at ever smaller scales. Click to enlarge Exactly what shape does this fern have?
The classical Euclidean geometry taught in high-school leaves us at a loss to answer this simple question. How can we describe a fern as a precise mathematical shape? 1. 2. Mandelbröt worked for IBM New York in the 1960s. 3. 4. Network science. {{Scienc[1] e}} Network science is an interdisciplinary academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks.
The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena. "[2] Background and history[edit] The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data.
In the 1930s Jacob Moreno, a psychologist in the Gestalt tradition, arrived in the United States. Department of Defense Initiatives[edit] In 2006, the U.S. Density[edit] Complex systems. Complex systems present problems both in mathematical modelling and philosophical foundations.
The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment.[1] Such systems are used to model processes in computer science, biology,[2] economics, physics, chemistry,[3] and many other fields. It is also called complex systems theory, complexity science, study of complex systems, sciences of complexity, non-equilibrium physics, and historical physics. A variety of abstract theoretical complex systems is studied as a field of mathematics. The key problems of complex systems are difficulties with their formal modelling and simulation.
Overview[edit] History[edit] A history of complexity science Typical areas of study[edit] Complexity management[edit] Complexity economics[edit] Complexity and modeling[edit] 1. Americas Europe.