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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
ubuntu2004
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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) 1996,1997

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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_FUNCTION_H

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#define __SGI_STL_FUNCTION_H

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#ifndef __STL_CONFIG_H

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#include <stl_config.h>

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#endif

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#ifndef __SGI_STL_INTERNAL_RELOPS

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#include <stl_relops.h>

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#endif

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#include <stddef.h>

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#ifndef __SGI_STL_INTERNAL_FUNCTION_H

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#include <stl_function.h>

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#endif

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#ifdef __STL_USE_NAMESPACE_FOR_RELOPS

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// Names from stl_relops.h

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using __STD_RELOPS::operator!=;

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using __STD_RELOPS::operator>;

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using __STD_RELOPS::operator<=;

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using __STD_RELOPS::operator>=;

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#endif /* __STL_USE_NAMESPACE_FOR_RELOPS */

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#ifdef __STL_USE_NAMESPACES

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// Names from stl_function.h

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using __STD::unary_function; 

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using __STD::binary_function; 

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using __STD::plus; 

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using __STD::minus; 

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using __STD::multiplies; 

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using __STD::divides; 

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using __STD::identity_element; 

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using __STD::modulus; 

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using __STD::negate; 

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using __STD::equal_to; 

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using __STD::not_equal_to; 

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using __STD::greater; 

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using __STD::less; 

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using __STD::greater_equal; 

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using __STD::less_equal; 

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using __STD::logical_and; 

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using __STD::logical_or; 

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using __STD::logical_not; 

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using __STD::unary_negate; 

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using __STD::binary_negate; 

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using __STD::not1; 

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using __STD::not2; 

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using __STD::binder1st; 

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using __STD::binder2nd; 

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using __STD::bind1st; 

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using __STD::bind2nd; 

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using __STD::unary_compose; 

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using __STD::binary_compose; 

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using __STD::compose1; 

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using __STD::compose2; 

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using __STD::pointer_to_unary_function; 

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using __STD::pointer_to_binary_function; 

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using __STD::ptr_fun; 

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using __STD::identity; 

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using __STD::select1st; 

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using __STD::select2nd; 

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using __STD::project1st; 

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using __STD::project2nd; 

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using __STD::constant_void_fun; 

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using __STD::constant_unary_fun; 

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using __STD::constant_binary_fun; 

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using __STD::constant0; 

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using __STD::constant1; 

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using __STD::constant2; 

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using __STD::subtractive_rng; 

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using __STD::mem_fun_t; 

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using __STD::const_mem_fun_t; 

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using __STD::mem_fun_ref_t; 

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using __STD::const_mem_fun_ref_t; 

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using __STD::mem_fun1_t; 

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using __STD::const_mem_fun1_t; 

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using __STD::mem_fun1_ref_t; 

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using __STD::const_mem_fun1_ref_t; 

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using __STD::mem_fun; 

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using __STD::mem_fun_ref; 

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using __STD::mem_fun1; 

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using __STD::mem_fun1_ref; 

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#endif /* __STL_USE_NAMESPACES */

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#endif /* __SGI_STL_FUNCTION_H */

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// Local Variables:

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// mode:C++

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// End:

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