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
 *

3
 * Copyright (c) 1994

4
 * Hewlett-Packard Company

5
 *

6
 * Permission to use, copy, modify, distribute and sell this software

7
 * and its documentation for any purpose is hereby granted without fee,

8
 * provided that the above copyright notice appear in all copies and

9
 * that both that copyright notice and this permission notice appear

10
 * in supporting documentation.  Hewlett-Packard Company makes no

11
 * representations about the suitability of this software for any

12
 * purpose.  It is provided "as is" without express or implied warranty.

13
 *

14
 *

15
 * Copyright (c) 1996,1997

16
 * Silicon Graphics Computer Systems, Inc.

17
 *

18
 * Permission to use, copy, modify, distribute and sell this software

19
 * and its documentation for any purpose is hereby granted without fee,

20
 * provided that the above copyright notice appear in all copies and

21
 * that both that copyright notice and this permission notice appear

22
 * in supporting documentation.  Silicon Graphics makes no

23
 * representations about the suitability of this software for any

24
 * purpose.  It is provided "as is" without express or implied warranty.

25
 */

26


27
#ifndef __SGI_STL_ALGO_H

28
#define __SGI_STL_ALGO_H

29


30
#include <algobase.h>

31
#include <tempbuf.h>

32
#include <stl_algo.h>

33
#include <stl_numeric.h>

34


35
#ifdef __STL_USE_NAMESPACES

36


37
// Names from <stl_algo.h>

38
using __STD::for_each; 

39
using __STD::find; 

40
using __STD::find_if; 

41
using __STD::adjacent_find; 

42
using __STD::count; 

43
using __STD::count_if; 

44
using __STD::search; 

45
using __STD::search_n; 

46
using __STD::swap_ranges; 

47
using __STD::transform; 

48
using __STD::replace; 

49
using __STD::replace_if; 

50
using __STD::replace_copy; 

51
using __STD::replace_copy_if; 

52
using __STD::generate; 

53
using __STD::generate_n; 

54
using __STD::remove; 

55
using __STD::remove_if; 

56
using __STD::remove_copy; 

57
using __STD::remove_copy_if; 

58
using __STD::unique; 

59
using __STD::unique_copy; 

60
using __STD::reverse; 

61
using __STD::reverse_copy; 

62
using __STD::rotate; 

63
using __STD::rotate_copy; 

64
using __STD::random_shuffle; 

65
using __STD::random_sample; 

66
using __STD::random_sample_n; 

67
using __STD::partition; 

68
using __STD::stable_partition; 

69
using __STD::sort; 

70
using __STD::stable_sort; 

71
using __STD::partial_sort; 

72
using __STD::partial_sort_copy; 

73
using __STD::nth_element; 

74
using __STD::lower_bound; 

75
using __STD::upper_bound; 

76
using __STD::equal_range; 

77
using __STD::binary_search; 

78
using __STD::merge; 

79
using __STD::inplace_merge; 

80
using __STD::includes; 

81
using __STD::set_union; 

82
using __STD::set_intersection; 

83
using __STD::set_difference; 

84
using __STD::set_symmetric_difference; 

85
using __STD::min_element; 

86
using __STD::max_element; 

87
using __STD::next_permutation; 

88
using __STD::prev_permutation; 

89
using __STD::find_first_of; 

90
using __STD::find_end; 

91
using __STD::is_sorted; 

92
using __STD::is_heap; 

93


94
// Names from stl_heap.h

95
using __STD::push_heap;

96
using __STD::pop_heap;

97
using __STD::make_heap;

98
using __STD::sort_heap;

99


100
// Names from <stl_numeric.h>

101
using __STD::accumulate; 

102
using __STD::inner_product; 

103
using __STD::partial_sum; 

104
using __STD::adjacent_difference; 

105
using __STD::power; 

106
using __STD::iota; 

107


108
#endif /* __STL_USE_NAMESPACES */

109


110
#endif /* __SGI_STL_ALGO_H */

111


112
// Local Variables:

113
// mode:C++

114
// End:

115


116