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Emergent Universe: Online Interactive Science Museum about Emergence. Scale invariance - Wikipedia, the free encyclopedia - StumbleUpon. Arnolds cat map - Wikipedia, the free encyclopedia - StumbleUpon. Picture showing how the linear map stretches the unit square and how its pieces are rearranged when the modulo operation is performed. The lines with the arrows show the direction of the contracting and expanding eigenspaces In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name.[1] Levitated Daily Source, the good source. Hyperchaos. A hyperchaotic attractor is typically defined as chaotic behavior with at least two positive Lyapunov exponents.

Hyperchaos

Co.combinatorics - Category theory, computational complexity, and combinatorics connections? - Theoretical Computer Science - Stack Exchange. I have been trying to read “Pearls of Functional Algorithm design”, and subsequently “The Algebra of Programming”, and there is an obvious correspondence between recursively (and polynomially) defined data types and combinatorial objects, having the same recursive definition and subsequently leading to the same formal power series (or generating functions), as shown in the introductions to combinatorial species (I read “Species and Functors and Types, Oh My!”).

co.combinatorics - Category theory, computational complexity, and combinatorics connections? - Theoretical Computer Science - Stack Exchange

So, for the first question, is there a way to recover the generating (recursive) equation from the power series? That’s an afterthought though. Circles within circles ] - StumbleUpon. The Art of Complex Problem Solving - StumbleUpon. Figures for &Impossible fractals& Figures for "Impossible fractals" Cameron Browne Figure 1.

Figures for &Impossible fractals&

Logical Paradoxes » The Barber Paradox. The Barber paradox is attributed to the British philosopher Bertrand Russell.

Logical Paradoxes » The Barber Paradox

It highlights a fundamental problem in mathematics, exposing an inconsistency in the basic principles on which mathematics is founded. The barber paradox asks us to consider the following situation: In a village, the barber shaves everyone who does not shave himself, but no one else. The question that prompts the paradox is this: Who shaves the barber? No matter how we try to answer this question, we get into trouble. If we say that the barber shaves himself, then we get into trouble.

Puzzles by Eric C. Harshbarger. In my mind a "puzzle" differs from a "game" in that the former is designed to be pretty much a solitary exercise, while the latter is meant to engage two or more people in some sort of competition.

Puzzles by Eric C. Harshbarger

On this page I'm listing various puzzles that I have invented. About complexity, complexity science map, complexity theory map, map complexity, geek t-shirts, math t-shirts, science t-shirts, computational modeling software, complexity map, statistics, social network analysis software, neural networking software - St.

Tag - Kolmogorov complexity - Jean-Christophe Dubacq. Levitated Daily Source, the good source. Self-organization. Figure 1: Snow Crystal.

Self-organization

In the beginning of quantum mechanics and statistical physics it was believed that a crystalline structure can be calculated by determining the minimum of the free energy. This may be true, e.g. for ionic crystals, such as sodium chloride, or metals. In this case, the Schrödinger equation for the ground state or possibly low lying states must be solved. Maze Design. We've been working on producing mazes by computer, with input from a human designer.

Maze Design

We're interested in two complementary questions with respect to maze design: Complexity: What makes a maze difficult to solve? The more we consider this question, the more elusive it becomes. It's certainly possible to begin defining mathematical measures of a maze's complexity, but complexity must depend on aspects of human perception as well. John Conways Game of Life - StumbleUpon. The Game The Game of Life is not your typical computer game.

John Conways Game of Life - StumbleUpon

It is a 'cellular automaton', and was invented by Cambridge mathematician John Conway. This game became widely known when it was mentioned in an article published by Scientific American in 1970. Complex interactions of simple agents. Complexity and Chaos Theory in Art - StumbleUpon. Complexity and Chaos Theory in Art by Jay Kappraff New Jersey Institute of Technology Newark NJ kappraff@aol.com.

Complexity and Chaos Theory in Art - StumbleUpon

- StumbleUpon. Non-equilibrium thermodynamics. Non-equilibrium thermodynamics is a branch of thermodynamics that deals with thermodynamic systems that are not in thermodynamic equilibrium.

Non-equilibrium thermodynamics

Most systems found in nature are not in thermodynamic equilibrium; for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.[1] Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Overview[edit] Excitable medium. An excitable medium is a nonlinear dynamical system which has the capacity to propagate a wave of some description, and which cannot support the passing of another wave until a certain amount of time has passed (known as the refractory time). A forest is an example of an excitable medium: if a wildfire burns through the forest, no fire can return to a burnt spot until the vegetation has gone through its refractory period and regrown. In Chemistry, oscillating reactions are excitable media, for example the Belousov–Zhabotinsky reaction and the Briggs–Rauscher reaction. Automaton. A self-operating machine Animatronics are a modern type of automata with electronics, often used for the portrayal of characters in films and in theme park attractions. Etymology[edit] The word "automaton" is the latinization of the Greek αὐτόματον, automaton, (neuter) "acting of one's own will".

This word was first used by Homer to describe automatic door opening,[2] or automatic movement of wheeled tripods.[3] It is more often used to describe non-electronic moving machines, especially those that have been made to resemble human or animal actions, such as the jacks on old public striking clocks, or the cuckoo and any other animated figures on a cuckoo clock. History[edit] Ancient[edit] The automata in the Hellenistic world were intended as tools, toys, religious idols, or prototypes for demonstrating basic scientific principles. Different Types of Complexity. Mandelbrot set. Initial image of a Mandelbrot set zoom sequence with a continuously colored environment Mandelbrot animation based on a static number of iterations per pixel. Gear Inventions and Artwork. Twistor theory. In theoretical and mathematical physics, twistor theory maps the geometric objects of conventional 3+1 space-time (Minkowski space) into geometric objects in a 4-dimensional space with metric signature (2,2).

This space is called twistor space, and its complex valued coordinates are called "twistors. " In 2003, Edward Witten[2] proposed uniting twistor and string theory by embedding the topological B model of string theory in twistor space. His objective was to model certain Yang-Mills amplitudes. The resulting model has come to be known as twistor string theory (read below). Simone Speziale and collaborators have also applied it to loop quantum gravity.[3] Details[edit] Sculpture - Unit Cube.