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) 1994
* Hewlett-Packard Company
*
* Permission to use, copy, modify, distribute and sell this software
* and its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation. Hewlett-Packard Company makes no
* representations about the suitability of this software for any
* purpose. It is provided "as is" without express or implied warranty.
*
*/
// Inclusion of this file is DEPRECATED. This is the original HP
// default allocator. It is provided only for backward compatibility.
// This file WILL BE REMOVED in a future release.
//
// DO NOT USE THIS FILE unless you have an old container implementation
// that requires an allocator with the HP-style interface.
//
// Standard-conforming allocators have a very different interface. The
// standard default allocator is declared in the header <memory>.
#ifndef DEFALLOC_H
#define DEFALLOC_H
#include <new.h>
#include <stddef.h>
#include <stdlib.h>
#include <limits.h>
#include <iostream.h>
#include <algobase.h>
template <class T>
inline T* allocate(ptrdiff_t size, T*) {
set_new_handler(0);
T* tmp = (T*)(::operator new((size_t)(size * sizeof(T))));
if (tmp == 0) {
cerr << "out of memory" << endl;
exit(1);
}
return tmp;
}
template <class T>
inline void deallocate(T* buffer) {
::operator delete(buffer);
}
template <class T>
class allocator {
public:
typedef T value_type;
typedef T* pointer;
typedef const T* const_pointer;
typedef T& reference;
typedef const T& const_reference;
typedef size_t size_type;
typedef ptrdiff_t difference_type;
pointer allocate(size_type n) {
return ::allocate((difference_type)n, (pointer)0);
}
void deallocate(pointer p) { ::deallocate(p); }
pointer address(reference x) { return (pointer)&x; }
const_pointer const_address(const_reference x) {
return (const_pointer)&x;
}
size_type init_page_size() {
return max(size_type(1), size_type(4096/sizeof(T)));
}
size_type max_size() const {
return max(size_type(1), size_type(UINT_MAX/sizeof(T)));
}
};
class allocator<void> {
public:
typedef void* pointer;
};
#endif