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.[1] Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. In the 19th century, Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. Mathematics, physics and chemistry can explain patterns in nature at different levels. History[edit] The American photographer Wilson Bentley (1865–1931) took the first micrograph of a snowflake in 1885.[10]

Trace theory In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation, analogous to the way that the free monoid provides the underpining for formal languages. The power of trace theory stems from the fact that the algebra of dependency graphs (such as Petri nets) is isomorphic to that of trace monoids, and thus, one can apply both algebraic formal language tools, as well as tools from graph theory. V.

Songs of Innocence and of Experience Songs of Innocence and of Experience is an illustrated collection of poems by William Blake. It appeared in two phases. A few first copies were printed and illuminated by William Blake himself in 1789; five years later he bound these poems with a set of new poems in a volume titled Songs of Innocence and of Experience Showing the Two Contrary States of the Human Soul. "Innocence" and "Experience" are definitions of consciousness that rethink Milton's existential-mythic states of "Paradise" and the "Fall." Blake's categories are modes of perception that tend to coordinate with a chronology that would become standard in Romanticism: childhood is a state of protected innocence rather than original sin, but not immune to the fallen world and its institutions. Songs of Innocence[edit] Songs of Innocence was originally a complete work first printed in 1789. The poems are each listed below: The Echoing Green The Lamb The Little Black Boy The Blossom The Chimney Sweeper The Little Boy found Infant Joy

Essential Math for Games Programmers As the quality of games has improved, more attention has been given to all aspects of a game to increase the feeling of reality during gameplay and distinguish it from its competitors. Mathematics provides much of the groundwork for this improvement in realism. And a large part of this improvement is due to the addition of physical simulation. Creating such a simulation may appear to be a daunting task, but given the right background it is not too difficult, and can add a great deal of realism to animation systems, and interactions between avatars and the world. This tutorial deepens the approach of the previous years' Essential Math for Games Programmers, by spending one day on general math topics, and one day focusing in on the topic of physical simulation. It, like the previous tutorials, provides a toolbox of techniques for programmers, with references and links for those looking for more information. Topics for the various incarnations of this tutorial can be found below. Slides

Rewriting In mathematics, computer science, and logic, rewriting covers a wide range of (potentially non-deterministic) methods of replacing subterms of a formula with other terms. What is considered are rewriting systems (also known as rewrite systems or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. Intuitive examples[edit] Logic[edit] In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be conveniently written as a rewriting system. (double negative elimination) (De Morgan's laws) (Distributivity) where the symbol ( Linguistics[edit] Abstract rewriting systems[edit] Example 1. , and y is irreducible. .

Yggdrasill Da Wikipedia, l'enciclopedia libera. Yggdrasill in un manoscritto islandese del XVII secolo. Yggdrasill [ˈygˌdrasilː], nella mitologia norrena, è l'albero cosmico, l'albero del mondo. Natura, struttura, funzione[modifica | modifica sorgente] Secondo Völuspá è un frassino (norreno askr); secondo Rodolfo di Fulda, monaco benedettino del IX secolo, che lo denomina come Irminsul[1] è invece un tasso o una quercia, (alberi comunque sacri presso i popoli del Nord Europa); il suo nome significa con ogni probabilità "cavallo di Yggr", dove "cavallo" è metafora per "forca", "patibolo", mentre Yggr è uno dei tanti nomi di Óðinn. Immenso, Yggdrasill sprofonda sin nel regno infero, mentre i suoi rami sostengono l'intera volta celeste. L'albero Yggdrasill è il luogo dell'assemblea (Thing) quotidiana degli Dèi che vi giungono cavalcando il ponte di Bifröst (l'Arcobaleno), vigilato dal dio Heimdallr. Altro nome dell'albero cosmico è Mímameiðr ("albero di Mími"). Note[modifica | modifica sorgente] Irminsul

Guerrilla Tool Development I have a weak spot for cool game development tools. Not the IDE, or art or sound tools – I mean the level editors, AI construction tools – those that developers develop specifically for their games. Those that you know could help you multiply your content, and craft your game just a little bit better. Unfortunately, if you work on a small team, developing sophisticated tools like that is pretty much out of the question. That does not mean you have to hardcode everything, though. Know your content creation tools inside out Before you even think about developing customised tools, it is extremely important to know your content-creation tools extremely well – even if you are not the content creator. As a programmer, you should focus on the following features: Automation Many art tools support some kind of batch processing. Data driven design This goes hand-in-hand with automation. Extensions Can you traverse the objects in the file? Organisation Layers Tree Templates Use appropriate file formats

Currying This article is about the mathematical technique. For the cooking process of this name, see Curry. For the leather finishing process, see Currier. Motivation[edit] Currying is similar to the process of calculating a function of multiple variables for some given values on paper. For example, given the function To evaluate , first replace with Since the result is a function of , this new function can be defined as Next, replace the argument with , producing On paper, using classical notation, this is usually done all in one step. If we let f be a function then the function h where is a curried version of . is the curried equivalent of the example above. Definition[edit] Given a function of type , currying it makes a function . takes an argument of type and returns a function of type . The → operator is often considered right-associative, so the curried function type is often written as . is equivalent to Mathematical view[edit] In a set-theoretic paradigm, currying is the natural correspondence between the set to

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