Botanique Algorithmique : Accueil
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. 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] In 1202, Leonardo Fibonacci (c 1170 – c 1250) introduced the Fibonacci number sequence to the western world with his book Liber Abaci.[5] Fibonacci gave an (unrealistic) biological example, on the growth in numbers of a theoretical rabbit population.[6] In 1917, D'Arcy Wentworth Thompson (1860–1948) published his book On Growth and Form. The American photographer Wilson Bentley (1865–1931) took the first micrograph of a snowflake in 1885.[10] Causes[edit] Types of pattern[edit] Symmetry[edit]
Trace theory
From Wikipedia, the free encyclopedia Theory of trace monoids 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 underpinning 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.
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." 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 Laughing Song The Divine Image Nurse's Song Infant Joy On Another's Sorrow Songs of Experience[edit] Blake's title plate (No.29) for Songs of Experience Earth's Answer The Clod and the Pebble The Little Girl Lost The Little Girl Found The Sick Rose The Tyger My Pretty Rose Tree
Constructal Theory and the Asynsis Principle | ASYNSIS
It’s with a sense of relief and vindication that work that I’ve previously termed Dynamical Symmetries or more recently, Asynsis (asymptotic synthesis), regarding optimal information, mass and energy flows in nature has also occurred in parallel, over a similar timeframe of 20-odd years. It’s called Constructal Law or Theory, if you prefer. The author of this research (which comes to similar conclusions), is the renowned Professor Adrian Bejan of the Pratt School of Mechanical Engineering at Duke University, NC, USA. He describes himself as an engineer and thermodynamicist as elaborated on here: The substantial and diverse academic work in the constructal field is to be found here: I also feel that our work is highly complementary in that he approached it as an engineer while I did as an architect. “Both positive and negative feedback loops effect a system.
La beauté des L-Systèmes - Ekino FR
You can also read this article in english. De quoi s’agit-il ? Un système de Lindenmayer (communément appelé L-système) est un modèle algorithmique récursif inspiré par la biologie et inventé en 1968 par le biologiste hongrois Aristid Lindenmayer. Il vise à fournir un moyen de modéliser la croissance de plantes et bactéries. Le concept fondamental des L-Systèmes est la réécriture, un procédé efficace permettant de générer des objets complexes en remplaçant simplement tout ou partie d’un objet initial. Nous pouvons envisager cela comme une cellule qui se divise à chaque itération afin de générer un organisme plus abouti. Si vous êtes curieux, wikipedia en fourni une description plus détaillée. Très bien, mais en quoi cela peut-il vous intéresser et, plus important encore, que peut-on en faire ? Il existe une multitude de cas d’usages, certains se sont même amusés à générer de la musique à partir de ceux-là, mais nous allons nous concentrer sur des applications visuelles. Qui va produire :
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. 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. Topics for the various incarnations of this tutorial can be found below. Current Materials Slides The latest available versions of the slides for the math tutorials at GDC 2015 are as follows: See below for further materials from past years that may be useful. Past Materials Presentations for the math tutorials at GDC 2014 are as follows: Presentations for the math tutorials (the physics presentations are available here) at GDC 2013 are as follows:
Rewriting
Replacing subterm in a formula with another term In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines,[1][2] or reduction systems). Rewriting can be non-deterministic. In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as a rewriting system.[6] The rules of an example of such a system would be: (double negation elimination) (De Morgan's laws) (distributivity) [note 1] where the symbol ( ) indicates that an expression matching the left hand side of the rule can be rewritten to one formed by the right hand side, and the symbols each denote a subexpression. For example, the computation of 2+2 to result in 4 can be duplicated by term rewriting as follows: where the rule numbers are given above the rewrites-to arrow. Abstract rewriting systems [edit] . . . implies . .
