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) 1997
* Silicon Graphics Computer Systems, Inc.
*
* 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. Silicon Graphics makes no
* representations about the suitability of this software for any
* purpose. It is provided "as is" without express or implied warranty.
*/
#ifndef __SGI_STL_CHAR_TRAITS_H
#define __SGI_STL_CHAR_TRAITS_H
#include <string.h>
#include <wchar.h>
#if defined(__STL_USE_NEW_IOSTREAMS) && !defined(__SGI_STL_IOSFWD)
#include <iosfwd>
#endif /* use new iostreams */
__STL_BEGIN_NAMESPACE
// Class __char_traits_base.
template <class _CharT, class _IntT> class __char_traits_base {
public:
typedef _CharT char_type;
typedef _IntT int_type;
#ifdef __STL_USE_NEW_IOSTREAMS
typedef streamoff off_type;
typedef streampos pos_type;
typedef mbstate_t state_type;
#endif /* __STL_USE_NEW_IOSTREAMS */
static void assign(char_type& __c1, const char_type& __c2) { __c1 = __c2; }
static bool eq(const _CharT& __c1, const _CharT& __c2)
{ return __c1 == __c2; }
static bool lt(const _CharT& __c1, const _CharT& __c2)
{ return __c1 < __c2; }
static int compare(const _CharT* __s1, const _CharT* __s2, size_t __n) {
for (size_t __i = 0; __i < __n; ++__i)
if (!eq(__s1[__i], __s2[__i]))
return __s1[__i] < __s2[__i] ? -1 : 1;
return 0;
}
static size_t length(const _CharT* __s) {
const _CharT __nullchar = _CharT();
size_t __i;
for (__i = 0; !eq(__s[__i], __nullchar); ++__i)
{}
return __i;
}
static const _CharT* find(const _CharT* __s, size_t __n, const _CharT& __c)
{
for ( ; __n > 0 ; ++__s, --__n)
if (eq(*__s, __c))
return __s;
return 0;
}
static _CharT* move(_CharT* __s1, const _CharT* __s2, size_t __n) {
memmove(__s1, __s2, __n * sizeof(_CharT));
return __s1;
}
static _CharT* copy(_CharT* __s1, const _CharT* __s2, size_t __n) {
memcpy(__s1, __s2, __n * sizeof(_CharT));
return __s1;
}
static _CharT* assign(_CharT* __s, size_t __n, _CharT __c) {
for (size_t __i = 0; __i < __n; ++__i)
__s[__i] = __c;
return __s;
}
static int_type not_eof(const int_type& __c) {
return !eq_int_type(__c, eof()) ? __c : 0;
}
static char_type to_char_type(const int_type& __c) {
return static_cast<char_type>(__c);
}
static int_type to_int_type(const char_type& __c) {
return static_cast<int_type>(__c);
}
static bool eq_int_type(const int_type& __c1, const int_type& __c2) {
return __c1 == __c2;
}
static int_type eof() {
return static_cast<int_type>(-1);
}
};
// Generic char_traits class. Note that this class is provided only
// as a base for explicit specialization; it is unlikely to be useful
// as is for any particular user-defined type. In particular, it
// *will not work* for a non-POD type.
template <class _CharT> class char_traits
: public __char_traits_base<_CharT, _CharT>
{};
// Specialization for char.
__STL_TEMPLATE_NULL class char_traits<char>
: public __char_traits_base<char, int>
{
public:
static char_type to_char_type(const int_type& __c) {
return static_cast<char_type>(static_cast<unsigned char>(__c));
}
static int_type to_int_type(const char_type& __c) {
return static_cast<unsigned char>(__c);
}
static int compare(const char* __s1, const char* __s2, size_t __n)
{ return memcmp(__s1, __s2, __n); }
static size_t length(const char* __s) { return strlen(__s); }
static void assign(char& __c1, const char& __c2) { __c1 = __c2; }
static char* assign(char* __s, size_t __n, char __c)
{ memset(__s, __c, __n); return __s; }
};
// Specialization for wchar_t.
__STL_TEMPLATE_NULL class char_traits<wchar_t>
: public __char_traits_base<wchar_t, wint_t>
{};
__STL_END_NAMESPACE
#endif /* __SGI_STL_CHAR_TRAITS_H */
// Local Variables:
// mode:C++
// End: