Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download

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.

2034 views
License: MIT
ubuntu2004
Tweet
Share
Share
1
/*

2
 * Copyright (c) 1996

3
 * Silicon Graphics Computer Systems, Inc.

4
 *

5
 * Permission to use, copy, modify, distribute and sell this software

6
 * and its documentation for any purpose is hereby granted without fee,

7
 * provided that the above copyright notice appear in all copies and

8
 * that both that copyright notice and this permission notice appear

9
 * in supporting documentation.  Silicon Graphics makes no

10
 * representations about the suitability of this software for any

11
 * purpose.  It is provided "as is" without express or implied warranty.

12
 *

13
 *

14
 * Copyright (c) 1994

15
 * Hewlett-Packard Company

16
 *

17
 * Permission to use, copy, modify, distribute and sell this software

18
 * and its documentation for any purpose is hereby granted without fee,

19
 * provided that the above copyright notice appear in all copies and

20
 * that both that copyright notice and this permission notice appear

21
 * in supporting documentation.  Hewlett-Packard Company makes no

22
 * representations about the suitability of this software for any

23
 * purpose.  It is provided "as is" without express or implied warranty.

24
 *

25
 */

26


27
#ifndef __SGI_STL_HASH_SET_H

28
#define __SGI_STL_HASH_SET_H

29


30
#ifndef __SGI_STL_INTERNAL_HASHTABLE_H

31
#include <stl_hashtable.h>

32
#endif 

33


34
#include <algobase.h>

35
#include <stl_hash_set.h>

36


37
#ifdef __STL_USE_NAMESPACES

38
using __STD::hash;

39
using __STD::hashtable;

40
using __STD::hash_set;

41
using __STD::hash_multiset;

42
#endif /* __STL_USE_NAMESPACES */

43


44
#endif /* __SGI_STL_HASH_SET_H */

45


46