Turbulence Flow visualization of a turbulent jet, made by laser-induced fluorescence. The jet exhibits a wide range of length scales, an important characteristic of turbulent flows. Laminar and turbulent water flow over the hull of a submarine In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time.
COMPLEXITY THEORY AND MANAGEMENT PRACTICE by JONATHAN ROSENHEAD | Home | Contents | Join the Discussion Forum | Rationale | Interesting Links | Feedback | Search | Jonathan Rosenhead There is some evidence of managerial take-up of ‘complexity’ as a framework for informing organisational practice. This is still at an early stage, and take-up may or may not lead to take-off. The purpose of this paper is to contribute to a discussion of the validity and significance of these ideas for the management of organisations.
Random walk Example of eight random walks in one dimension starting at 0. The plot shows the current position on the line (vertical axis) versus the time steps (horizontal axis). A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905. Random walks have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry, and biology. Random walks explain the observed behaviors of processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity. Various different types of random walks are of interest.
Sacred geometry As worldview and cosmology The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). Golden ratio Line segments in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number. Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below).
Patterns in nature Natural patterns form as wind blows sand in the dunes of the Namib Desert. The crescent shaped dunes and the ripples on their surfaces repeat wherever there are suitable conditions. Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, arrays, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature.
Fractal flame Fractal flames differ from ordinary iterated function systems in three ways: Nonlinear functions are iterated instead of affine transforms.Log-density display instead of linear or binary (a form of tone mapping)Color by structure (i.e. by the recursive path taken) instead of monochrome or by density. The tone mapping and coloring are designed to display as much of the detail of the fractal as possible, which generally results in a more aesthetically pleasing image. Algorithm The algorithm consists of two steps: creating a histogram and then rendering the histogram. Creating the histogram
Fractal art Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. Fractal art developed from the mid-1980s onwards. It is a genre of computer art and digital art which are part of new media art. The Julia set and Mandelbrot sets can be considered as icons of fractal art. Fractal art (especially in the western world) is not drawn or painted by hand. It is usually created indirectly with the assistance of fractal-generating software, iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product.
Snowflake Snowflake viewed in an optical microscope A snowflake is either a single ice crystal or an aggregation of ice crystals which falls through the Earth's atmosphere. They begin as snow crystals which develop when microscopic supercooled cloud droplets freeze. Snowflakes come in a variety of sizes and shapes. Complex shapes emerge as the flake moves through differing temperature and humidity regimes, such that individual snowflakes are nearly unique in structure. Snowflakes encapsulated in rime form balls known as graupel.
Download Fractint 18.21 Free - Create your fractals with the help of this tool. The beauty and complexity of fractals has ensnared many users and not necessarily those with inclinations towards the exact sciences. Nonetheless, looking deep inside one or customizing its parameters would not be possible without the help of a utility like Fractint. Dull interface for splendid shapes With the package unwrapped, you can start the application immediately as it doesn't have to be installed and comes with all the necessary dependencies. List of fractals by Hausdorff dimension Deterministic fractals Random and natural fractals See also Mandelbulb The Mandelbulb is a three-dimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions. However, this set does not exhibit detail at all scales like the 2D Mandelbrot set does. White and Nylander's formula for the "nth power" of the 3D vector
Sterling2 download page Sterling2 is based on Sterling, a fractal-generating program written in 1999 by the redoubtable Stephen C. Ferguson. In mid-2007 I contacted Stephen, as I thought that Sterling was an excellent program that lacked one key feature - a formula editor. Crystal The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word crystal is derived from the Ancient Greek word κρύσταλλος (krustallos), meaning both “ice” and “rock crystal”, from κρύος (kruos), "icy cold, frost".