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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.

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License: MIT
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/*

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 *

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 * Copyright (c) 1994

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 * Hewlett-Packard Company

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 *

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 * Permission to use, copy, modify, distribute and sell this software

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 * and its documentation for any purpose is hereby granted without fee,

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 * provided that the above copyright notice appear in all copies and

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 * that both that copyright notice and this permission notice appear

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 * in supporting documentation.  Hewlett-Packard Company makes no

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 * representations about the suitability of this software for any

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 * purpose.  It is provided "as is" without express or implied warranty.

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 *

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 *

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 * Copyright (c) 1996

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 * Silicon Graphics Computer Systems, Inc.

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 *

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 * Permission to use, copy, modify, distribute and sell this software

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 * and its documentation for any purpose is hereby granted without fee,

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 * provided that the above copyright notice appear in all copies and

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 * that both that copyright notice and this permission notice appear

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 * in supporting documentation.  Silicon Graphics makes no

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 * representations about the suitability of this software for any

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 * purpose.  It is provided "as is" without express or implied warranty.

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 */

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#ifndef __SGI_STL_ITERATOR_H

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#define __SGI_STL_ITERATOR_H

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#ifndef __SGI_STL_FUNCTION_H

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#include <function.h>

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#endif

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#include <stddef.h>

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#ifdef __STL_USE_NEW_IOSTREAMS 

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#include <iosfwd>

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#else /* __STL_USE_NEW_IOSTREAMS */

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#include <iostream.h>

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#endif /* __STL_USE_NEW_IOSTREAMS */

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#ifndef __SGI_STL_INTERNAL_ITERATOR_BASE_H

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#include <stl_iterator_base.h>

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#endif

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#ifndef __SGI_STL_INTERNAL_ITERATOR_H

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#include <stl_iterator.h>

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#endif

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#ifndef __TYPE_TRAITS_H

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#include <type_traits.h>

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#endif

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#ifndef __SGI_STL_INTERNAL_CONSTRUCT_H

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#include <stl_construct.h>

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#endif

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#ifndef __SGI_STL_INTERNAL_RAW_STORAGE_ITERATOR_H

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#include <stl_raw_storage_iter.h>

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#endif

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#ifdef __STL_USE_NAMESPACES

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// Names from stl_iterator.h

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using __STD::input_iterator_tag;

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using __STD::output_iterator_tag;

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using __STD::forward_iterator_tag;

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using __STD::bidirectional_iterator_tag;

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using __STD::random_access_iterator_tag;

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#if 0

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using __STD::iterator;

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#endif

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using __STD::input_iterator;

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using __STD::output_iterator;

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using __STD::forward_iterator;

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using __STD::bidirectional_iterator;

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using __STD::random_access_iterator;

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#ifdef __STL_CLASS_PARTIAL_SPECIALIZATION

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using __STD::iterator_traits;

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#endif

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using __STD::iterator_category;

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using __STD::distance_type;

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using __STD::value_type;

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using __STD::distance; 

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using __STD::advance; 

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using __STD::insert_iterator;

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using __STD::front_insert_iterator;

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using __STD::back_insert_iterator;

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using __STD::inserter;

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using __STD::front_inserter;

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using __STD::back_inserter;

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using __STD::reverse_iterator;

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using __STD::reverse_bidirectional_iterator;

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using __STD::istream_iterator;

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using __STD::ostream_iterator;

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// Names from stl_construct.h

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using __STD::construct;

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using __STD::destroy;

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// Names from stl_raw_storage_iter.h

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using __STD::raw_storage_iterator;

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#endif /* __STL_USE_NAMESPACES */

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#endif /* __SGI_STL_ITERATOR_H */

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// Local Variables:

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// mode:C++

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// End:

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