Apoptosis. In contrast to necrosis, which is a form of traumatic cell death that results from acute cellular injury, in general apoptosis confers advantages during an organism's lifecycle. For example, the separation of fingers and toes in a developing human embryo occurs because cells between the digits apoptose. Unlike necrosis, apoptosis produces cell fragments called apoptotic bodies that phagocytic cells are able to engulf and quickly remove before the contents of the cell can spill out onto surrounding cells and cause damage.[5] Research in and around apoptosis has increased substantially since the early 1990s. In addition to its importance as a biological phenomenon, defective apoptotic processes have been implicated in an extensive variety of diseases. Excessive apoptosis causes atrophy, whereas an insufficient amount results in uncontrolled cell proliferation, such as cancer. Discovery and etymology[edit] German scientist Carl Vogt was first to describe the principle of apoptosis in 1842.
Mathematics Archives. The Math Forum - Cellular Automata. Automata theory. An example of an automaton. The study of the mathematical properties of such automata is automata theory. Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science, under Discrete mathematics (a section of Mathematics and also of Computer Science).
Automata comes from the Greek word αὐτόματα meaning "self-acting". Automata theory is also closely related to formal language theory. Automata play a major role in theory of computation, compiler design, artificial intelligence, parsing and formal verification. Automata[edit] Following is an introductory definition of one type of automaton, which attempts to help one grasp the essential concepts involved in automata theory(s). Informal description[edit] In short, an automaton is a mathematical object that takes a word as input and decides either to accept it or reject it. Formal definition[edit] Automaton Input word Run Input States. Langton's Ants. Langton's Ant. Brian's Brain. A typical chaotic Brian's Brain pattern showing spaceships, rakes and diagonal waves. In this animation, the on cells are white and the dying cells are blue.
Because of the cellular automaton's name, some websites compare the automaton to a brain and each of its cells to a neuron, which can be in three different states: ready (off), firing (on), and refractory (dying).[1][2] Resnick, Mitchel; Silverman, Brian (1996-02-04). "Exploring Emergence: The Brain Rules". MIT Media Laboratory, Lifelong Kindergarten Group. Conway's Game of Life. Life32. Conway's Game of Life freeware for Windows9x/NT/2000/XP Version 2.15, last updated August 10, 2002. There is a European mirror of this page in Holland: Please send questions and comments on Life32 to Johan Bontes (jbontes@xs4all.nl) Download Life32 version 2.15 ... from an FTP site in California: zip file ... from an FTP site in Wisconsin: zip file ... from an FTP site in Atlanta: zip file ... from a web-site in Holland: zip file The self-installing .exe uses InstallShield to make installation a breeze.
If you don't have a program to handle zip files, have a look at Winzip (shareware) or UltimateZip (freeware). Downloaded the thing and still have questions? What does Life32 do? Life32 is a player for Conway's game of life and related cellular automa. Here is a screenshot: In short, Life32 is the best, fastest, and most user-friendly life player around. Universe size is 1 million x 1 million. Get DirectX! Life32 works best when used with Microsoft's DirectX. Mirek's Cellebration. Visual Automata Simulator. Main Page - LifeWiki. Stephen Wolfram. Stephen Wolfram (born 29 August 1959) is a British scientist,[7] known for his work in theoretical physics, as the chief designer of the Mathematica software application and the Wolfram Alpha answer engine, as well as the CEO of Wolfram Research, and the author of A New Kind of Science.[2][8][9][10][11][12][13] Background[edit] Wolfram's parents were Jewish refugees who emigrated from Germany to England in the 1930s.[5][14] Wolfram's father Hugo was a textile manufacturer and novelist (Into a Neutral Country) and his mother Sybil was a professor of philosophy at the University of Oxford.[15] He has a younger brother, Conrad Wolfram.[16] Wolfram is married to a mathematician and has four children.[17] Education[edit] Wolfram was educated at Eton College, but left prematurely in 1976.
Career[edit] Following his PhD, Wolfram joined the faculty at Caltech and received one of the first MacArthur Fellowships in 1981, at age 21.[18] Research[edit] Unpublished works[edit] Particle physics[edit] John Horton Conway. John Horton Conway (born 26 December 1937) is a British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Biography[edit] Conway's parents were Agnes Boyce and Cyril Horton Conway. He was born in Liverpool.[4] He became interested in mathematics at a very early age and his mother recalled that he could recite the powers of two when he was four years old.
At the age of eleven his ambition was to become a mathematician. After leaving secondary school, Conway entered Gonville and Caius College, Cambridge to study mathematics. He left Cambridge in 1986 to take up the appointment to the John von Neumann Chair of Mathematics at Princeton University. Conway resides in Princeton, New Jersey. Achievements[edit] Combinatorial game theory[edit] Geometry[edit] Geometric topology[edit] J.H. Game of Life Status page. [< < Back to main page] Last updated: 28 Aug. 2013 Last reviewed: 28 Aug. 2013 This page documents what is known and what is not known in the Game of Life concerning certain classes of patterns. If you find an error on this page, please let me know. For definitions of the terms used on this page, see Stephen Silver's Life Lexicon (listed here). This page requires a browser that can display table cells and text with colored backgrounds.
Reference collection Here's a collection of examples of most of the objects that this page claims are known: life-status.zip (last updated 3 Jun. 2013) It does not include: Most c/2 technology. Contents Some sections include historical notes that list one or more discoverers with the more recent discoveries. Oscillator periods For green status, an oscillator must have a cell that oscillates at the full period, rather than some smaller factor of that period.
Yellow means that the only known examples contain no cells that oscillate at the full period. The "Gun? " Jason’s Life Page. Treasure Trove of the Life C.A. Life Lexicon. This is the home page of Stephen Silver's Life Lexicon, an explanation of over seven hundred terms used in Conway's Life. The Life Lexicon may be copied, modified and distributed under the terms of the Creative Commons Attribution-ShareAlike 3.0 Unported licence (CC BY-SA 3.0). You can view the Life Lexicon on-line, or download it in various forms, as shown in the table below. If you want the Lexicon in HTML, note that the single-page version can be difficult to use on some older systems due to its size, in which case you may prefer to use the multipage version. If you are a GNU Emacs user, then the ASCII version with its lifelex.el is recommended. Note that the source distribution consists of the ASCII version plus the files needed to generate the HTML versions.
A Russian translation of the Life Lexicon by Nicolay Beluchenko is also available. Every other author may aspire to praise; the lexicographer can only hope to escape reproach. To My Life Page. Achim's Game of Life Page. Introduction Game of Life is a cellular automaton on an infinite quadratic grid. Each grid cell is either alive/on or dead/off. The new state of each cell is computed in discrete timesteps and is determinated by it's old state and the sum of the alive cells among its surrounding 8 nearest neighbours cells. All these changes are simultaneously over the whole, infinite grid! The Game of Life rules let a cell in the next generation only alive if a living cell is either surrounded by either 2 or 3 alive cells, the survive condition, or a dead cell flips into the alive state in the next generation if it is surrounded by exactly 3 living cells, the borne condition.
A 143-bit Garden Of Eden object , constructed January 1991. Collected Resources There is nothing as interesting as Life ! Back to my HomePage. Wireworlds. Wireworld Player. Family Tree. 3D Genetic Topology (requires Java) (a work in progress - for SyStemma, LLC) The above visualization is a work-in-progress. It shows a variation of the classic genogram, used in family research, extended into 3 dimensions, where the third dimension (vertical) is time. It borrows some of the conventions of the genogram, such as squares and circles representing males and females, but diverges in other ways. Family researchers James H. Thus began a research project, based in what was then the Advanced Graphics Research Lab at Syracuse University. The above 3D model is a bare-bones framewok, and in no way represents the vast potential of using such a technique to visualize multi-generational family process.
James H. (c)copyright 2005, by James H. Wiresq. Xlife. Xlife is a laboratory for experimenting with cellular automata. It supports loadable rulesets and palettes, different topologies, and up to 256-state cellular automata. It has rules and patterns for Life, Brian's Brain, Perrier's Loops, Langton's Ants and Loops, Wireworld, E.F. Codd's 1975 UCC automaton, some Prisoner's Dilemma games, and many others. It is very fast for step-by-step mode, bounded grid, and chaotic patterns. It has several unique features: a historical mode, a pseudocolor mode, and n-state statistics. It has been developed since 1989. Recent releases Release Notes: Fast history record mode, fast oscillator check mode, speed indicator, more supported types of automata, a faster video subsystem, a lot of small improvements and fixes,... and a new 'gen-multirules' utility to generate competing n-state rules for 2-state automata Release Notes: This release adds new pseudocolor mode, makes Xlife a bit faster and smoother, and fixes several errors.
Golly Game of Life. The Powder Toy. Sculpt Create landscapes and cities ... then blow them up! Browse and search ... through thousands of saves created by the community, upload your own! Create Build needlessly complex machines to do simple tasks ... then blow them up! Have you ever wanted to blow something up? The Powder Toy is a free physics sandbox game, which simulates air pressure and velocity, heat, gravity and a countless number of interactions between different substances! There is a Lua API – you can automate your work or even make plugins for the game. Necro Bones. Eden.