One-dimensional cellular automata. One-dimensional cellular automata You are encouraged to solve this task according to the task description, using any language you may know.
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death. [edit] ACL2 [edit] Ada [edit] ALGOL 68 [edit] Using the low level packed arrays of BITS manipulation operators Output: [edit] AutoHotkey. Diehard tests. The diehard tests are a battery of statistical tests for measuring the quality of a random number generator.
They were developed by George Marsaglia over several years and first published in 1995 on a CD-ROM of random numbers. These are the tests: See also[edit] External links[edit] Cellular Automaton. A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells.
The rules are then applied iteratively for as many time steps as desired. von Neumann was one of the first people to consider such a model, and incorporated a cellular model into his "universal constructor. " Cellular automata were studied in the early 1950s as a possible model for biological systems (Wolfram 2002, p. 48). Comprehensive studies of cellular automata have been performed by S. Wolfram starting in the 1980s, and Wolfram's fundamental research in the field culminated in the publication of his book A New Kind of Science (Wolfram 2002) in which Wolfram presents a gigantic collection of results concerning automata, among which are a number of groundbreaking new discoveries.
Cellular automata come in a variety of shapes and varieties. -dimensional integer lattice colors. . Elementary Cellular Automaton. The simplest class of one-dimensional cellular automata.
Elementary cellular automata have two possible values for each cell (0 or 1), and rules that depend only on nearest neighbor values. As a result, the evolution of an elementary cellular automaton can completely be described by a table specifying the state a given cell will have in the next generation based on the value of the cell to its left, the value the cell itself, and the value of the cell to its right. Since there are possible binary states for the three cells neighboring a given cell, there are a total of elementary cellular automata, each of which can be indexed with an 8-bit binary number (Wolfram 1983, 2002). ) is illustrated above. Generations of elementary cellular automaton rule are implemented as CellularAutomaton[r, , n, All, All The illustrations above show some automata numbers that give particularly interesting pattern propagated for 15 generations starting with a single black cell in the initial iteration.
Rule 30. One of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002).
It specifies the next color in a cell, depending on its color and its immediate neighbors. Its rule outcomes are encoded in the binary representation . This rule is illustrated above together with the evolution of a single black cell it produces after 15 steps (Wolfram 2002, p. 55). 250 iterations of rule 30 are illustrated above. Starting with a single black cell, successive generations are given by interpreting the numbers 1, 7, 25, 111, 401, 1783, 6409, 28479, 102849, ... Rule 30 is the mirror image, complement, and mirror complement of rules 86, 135, and 149, respectively. Rule 30 is of special interest because it is chaotic (Wolfram 2002, p. 871), with central column given by 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, ...
Jen (1990) proved that with the initial state of a single black cell, the sequence of colors attained in any two adjacent cells is not periodic (Gray 2003).