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Brian's Brain
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule. Rules Brian's Brain consists of an infinite two-dimensional grid of cells, but unlike Seeds, each cell may be in one of three states: on, dying, or off. Each cell is considered to have eight neighbors (the Moore neighborhood), as in Seeds and Conway's Game of Life. In each time step, a cell turns on if it was off but had exactly two neighbors that were on, just like the birth rule for Seeds. All cells that were "on" go into the "dying" state, which is not counted as an "on" cell in the neighbor count, and prevents any cell from being born there. Cells that were in the dying state go into the off state. Behavior 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). The "dying state" cells tend to lead to directi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian's Brain
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule. Rules Brian's Brain consists of an infinite two-dimensional grid of cells, but unlike Seeds, each cell may be in one of three states: on, dying, or off. Each cell is considered to have eight neighbors (the Moore neighborhood), as in Seeds and Conway's Game of Life. In each time step, a cell turns on if it was off but had exactly two neighbors that were on, just like the birth rule for Seeds. All cells that were "on" go into the "dying" state, which is not counted as an "on" cell in the neighbor count, and prevents any cell from being born there. Cells that were in the dying state go into the off state. Behavior 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). The "dying state" cells tend to lead to directi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian Silverman
Brian Silverman is a Canadian computer scientist, the creator of many programming environments for children,Computing Pioneer Returns to CMK 2010 Faculty! , Constructing Modern Knowledge, September 29, 2010. and a researcher in . Silverman was a student at the in the 1970s, where he was one of the creators of a computer that pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seeds (cellular Automaton)
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells, each of which may be in one of two states: ''on'' or ''off''. Each cell is considered to have eight neighbors (Moore neighborhood), as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S. In Game of Life terminology, a pattern in which all cells that were on turn off at each step is called a ''phoenix''. All patterns in Seeds have this form. Even though all live cells are constantly dying, the small birth requirement of two cells means that nearly every pattern in Seeds explodes into a chaotic mess that grows to cover the entire universe. Thus, in Wolfram's classificatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moore Neighborhood
In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it. Name The neighborhood is named after Edward F. Moore, a pioneer of cellular automata theory. Importance It is one of the two most commonly used neighborhood types, the other one being the von Neumann neighborhood, which excludes the corner cells. The well known Conway's Game of Life, for example, uses the Moore neighborhood. It is similar to the notion of 8-connected pixels in computer graphics. The Moore neighbourhood of a cell is the cell itself and the cells at a Chebyshev distance of 1. The concept can be extended to higher dimensions, for example forming a 26-cell cubic neighborhood for a cellular automaton in three dimensions, as used by 3D Life. In dimension ''d,'' where 0 \le d, d \in \mathbb, the size of the neighborhood is 3''d'' − 1. In two dimensions, the number of cells in an ''ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway's Game Of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine. Rules The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of square ''cells'', each of which is in one of two possible states, ''live'' or ''dead'' (or ''populated'' and ''unpopulated'', respectively). Every cell interacts with its eight ''neighbours'', which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur: # Any live cell with fewer than two live neighbours dies, as if by underpopulation. # Any live cell with two or three live nei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spaceship (cellular Automaton)
In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship. Description The speed of a spaceship is often expressed in terms of ''c'', the metaphorical speed of light (one cell per generation) which in many cellular automata is the fastest that an effect can spread. For example, a glider in Conway's Game of Life is said to have a speed of c/4, as it takes four generations for a given state to be translated by one cell. Similarly, the ''lightweight spaceship'' is said to have a speed of c/2, as it takes four generations for a given state to be translated by two cells. More generally, if a spaceship in a 2D automaton with the Moore neighborhood is translated by (x, y) after n generations, then the speed v is defined as: This notation can be readily generalised to cellular automata with di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rake (cellular Automaton)
A rake, in the lexicon of cellular automata, is a type of ''puffer train'', which is an automaton that leaves behind a trail of debris. In the case of a rake, however, the debris left behind is a stream of spaceships, which are automata that "travel" by looping through a short series of iterations and end up in a new location after each cycle returns to the original configuration. In Conway's Game of Life, the discovery of rakes was one of the key components needed to form the ''breeder'', the first known pattern in Life in which the number of live cells exhibits quadratic growth. A breeder is formed by arranging several rakes so that the '' gliders''—the smallest possible spaceships—they generate interact to form a sequence of '' glider guns'', patterns which emit gliders. The emitted gliders fill a growing triangle of the plane of the game. More generally, when a rake exists for a cellular automaton rule (a mathematical function defining the next iteration to be derived f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light (cellular Automaton)
In Conway's Game of Life (and related cellular automata), the speed of light is a propagation rate across the grid of exactly one step (either horizontally, vertically or diagonally) per generation. In a single generation, a cell can only influence its nearest neighbours, and so the speed of light (by analogy with the speed of light in physics) is the maximum rate at which information can propagate. It is therefore an upper bound to the speed at which any pattern can move. Notation As in physics, the speed of light is represented with the letter ''c''. This in turn is used as a reference for describing the average propagation speed of any given type of spaceship. For example, a glider is said to have a speed of ''c''/4, as it takes four generations for a given state to be translated by one cell. Similarly, the "lightweight spaceship" is said to have a speed of ''c''/2, as it takes four generations for a given state to be translated by two cells. Lightspeed propagation While ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillator (cellular Automaton)
In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely. Depending on context, the term may also include spaceships as well. The smallest number of generations it takes before the pattern returns to its initial condition is called the ''period'' of the oscillator. An oscillator with a period of 1 is usually called a still life, as such a pattern never changes. Sometimes, still lifes are not taken to be oscillators. Another common stipulation is that an oscillator must be finite. Examples In Conway's Game of Life, finite oscillators are known to exist for all periods except 19 and 41. Additionally, until July 2022, the only known examples for period 34 were considered trivial because they consisted of essentially separate components that oscillate at smaller periods. For instance, one can create a period 34 osc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mitchel Resnick
Mitchel Resnick (born June 12, 1956) is LEGO Papert Professor of Learning Research, Director of the Okawa Center, and Director of the Lifelong Kindergarten group at the Massachusetts Institute of Technology (MIT) Media Lab. , Resnick serves as head of the Media Arts and Sciences academic program, which grants master's degrees and Ph.D.s at the MIT Media Lab. Resnick's research group has developed a variety of educational tools that engage people in new types of design activities and learning experiences, including the ''Programmable Bricks'' that were the basis for the award-winning Lego Mindstorms and StarLogo software. He cofounded the Computer Clubhouse, an award-winning network of learning centers for youth from under-served communities. Resnick is also a cofounder and a co-principal investigator of the Center for Civic Media at MIT. Resnick's group has developed a new computer programming language, named Scratch, that makes it easier for children to create animated stor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
