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Fractal

Fractal
Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable.[2][5][8] An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.[7]:48[2]:15 There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Introduction[edit] The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. History[edit] Figure 2.

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Metacognition Metacognition is defined as "cognition about cognition", or "knowing about knowing". It comes from the root word "meta", meaning beyond.[1] It can take many forms; it includes knowledge about when and how to use particular strategies for learning or for problem solving.[1] There are generally two components of metacognition: knowledge about cognition, and regulation of cognition.[2] Metamemory, defined as knowing about memory and mnemonic strategies, is an especially important form of metacognition.[3] Differences in metacognitive processing across cultures have not been widely studied, but could provide better outcomes in cross-cultural learning between teachers and students.[4] Simplexity Simplexity is an emerging theory that proposes a possible complementary relationship between complexity and simplicity. The term draws from General Systems Theory, Dialectics (philosophy) and Design. Jeffrey Kluger wrote a book about this phenomenon that describes how house plants can be more complicated than industrial plants, how a truck driver's job can be as difficult as a CEO's and why 90% of the money donated to help cure diseases are given only to the research of 10% of them (and vice versa). The term has been adopted in advertising, marketing and the manufacture of left-handed screwdrivers. Design aspects[edit] Complexity tends to rise as system elements specialize and diversify to solve specific challenges.Simple interfaces tend to improve the usability of complex systems.

Fractals: A Sense of Scale By Peter Tyson Posted 10.01.08 NOVA So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ad infinitum. —Jonathan Swift, from "On Poetry: A Rhapsody" The satirist and author of Gulliver's Travels might have been talking about fractals when he made this oft-quoted observation—if he hadn't lived two centuries before fractals were discovered.

Faust Faust is the protagonist of a classic German legend. He is a scholar who is highly successful yet dissatisfied with his life, which leads him to make a pact with the Devil, exchanging his soul for unlimited knowledge and worldly pleasures. The Faust legend has been the basis for many literary, artistic, cinematic, and musical works that have reinterpreted it through the ages. "Faust" and the adjective "Faustian" imply a situation in which an ambitious person surrenders moral integrity in order to achieve power and success for a delimited term.[1][2] Summary of the story[edit]

Supervenience The upper levels on this chart can be considered to supervene on the lower levels. In philosophy, supervenience is an ontological relation that is used to describe cases where (roughly speaking) the lower-level properties of a system determine its higher level properties. Some philosophers hold that the world is structured in to a kind of hierarchy of properties, where the higher level properties supervene on the lower level properties.

The human microbiome: Me, myself, us WHAT’S a man? Or, indeed, a woman? Biologically, the answer might seem obvious. A human being is an individual who has grown from a fertilised egg which contained genes from both father and mother. A growing band of biologists, however, think this definition incomplete. They see people not just as individuals, but also as ecosystems. Twin Prime Conjecture PBS Airdate: January 10, 2006 ROBERT KRULWICH: Our next story concerns prime numbers. It's a mystery that's been around for 2,300 years, since the days of the great mathematician Euclid. Now a prime number, for those of you who have forgotten, is a number which can only be divided by itself and one. And there is this curious thing about primes. They seem for some reason to clump together.

Fractal Architecture by Michael Ostwald for the Nexus Network Journal vol.3 no.1 Winter 2001 Michael J. OstwaldDepartment of Architecture Faculty of Architecture, Building and Design, University of Newcastle University Drive, Callaghan, NSW 2308 AUSTRALIA INTRODUCTIONFor more than two decades an intricate and contradictory relationship has existed between architecture and the sciences of complexity. While the nature of this relationship has shifted and changed throughout that time a common point of connection has been fractal geometry. Fideism Fideism is an epistemological theory which maintains that faith is independent of reason, or that reason and faith are hostile to each other and faith is superior at arriving at particular truths (see natural theology). The word fideism comes from fides, the Latin word for faith, and literally means "faith-ism.

Think Complexity by Allen B. Downey Buy this book from Amazon.com. Download this book in PDF. A Radical Mind Posted 10.01.08 NOVA "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says.

are you a fractaloid, or a euclinaut? euclidean bound guesses verses, the infinite iris of the fractal by hyperevolution Jul 21

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