A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.
This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.
License: MIT
ubuntu2004
/* * Copyright (C) 2004 Bryant Lee * * This file is part of FPeriod. * * FPeriod is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * FPeriod is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with FPeriod; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA */ /* String Ops * Some operations that can be performed on strings * * Written by: Bryant Lee * Date: 10/29/04 */ #ifndef STRING_OPS_H #define STRING_OPS_H #define byte unsigned char #include <string> #include <vector> void split(const string &str, char c, vector<string> &output); void trim(string &str); //returns true if c is an upper or lower case letter bool alphachar(char c); //copy a byte array void copyWord(byte *a, byte *b, unsigned int length); void copyUIntArray(unsigned int *a, unsigned int *b, unsigned int length); void printArray(byte *arr, unsigned int length); void printUInt(unsigned int word, unsigned int length); void printUIntArray(unsigned int word[], unsigned int length); bool iterateWord(byte* arr, unsigned int length, unsigned int shiftSize); #endif