1Math::PlanePath::DekkinUgsCeerntCroenst(r3i)buted Perl DMoactuhm:e:nPtlaatnieoPnath::DekkingCentres(3)
2
6 Math::PlanePath::DekkingCentres -- 5x5 self-similar
7
9 use Math::PlanePath::DekkingCentres;
10 my $path = Math::PlanePath::DekkingCentres->new;
11 my ($x, $y) = $path->n_to_xy (123);
12
14 This is a variation on a 5x5 self-similar curve from
15 F. M. Dekking, "Recurrent Sets", Advances in Mathematics, volume
17 44, 1982, pages 79-104, section 4.9 "Gosper-Type Curves"
18 and which is a horizontal mirror image of the E-curve of McKenna 1978.
20 The form visits the "centres" of the 5x5 self-similar unit squares of
22 the pattern. The result is some diagonal steps, but replications
23 wholly within 5x5 areas.
24 ...
26 | /
27 9 | 115-116 122-123-124 89--88 86--85--84
28 | | | \ | \ | |
29 8 | 114 117-118 121-120 90 92 87 82--83
30 | | \ / |/ \ |
31 7 | 113-112 106 119 102 91 94--93 81 77
32 | / / | / | / / / |
33 6 | 111 107 105 103 101 95--96 80 78 76
34 | | \ \ | | \ \ | |
35 5 | 110-109-108 104 100--99--98--97 79 75
36 | \
37 4 | 10--11 13--14--15 35--36 38--39--40 74 70 66--65--64
38 | | \ | | | \ | | | |\ \ |
39 3 | 9 7 12 17--16 34 32 37 42--41 73 71 69 67 63
40 | |/ \ | |/ \ | |/ |/ /
41 2 | 8 5-- 6 18 22 33 30--31 43 47 72 55 68 62--61
42 | / / / | / / / | / \ |
43 1 | 4-- 3 19 21 23 29--28 44 46 48 54--53 56--57 60
44 | \ \ | | \ \ | | \ | |
45 Y=0 | 0-- 1-- 2 20 24--25--26--27 45 49--50--51--52 58--59
46 +---------------------------------------------------------------
47 X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
48 The base pattern is the N=0 to N=24 section. It repeats with rotations
50 or reversals which make the ends join. For example N=75 to N=99 is the
51 base pattern in reverse. Or N=50 to N=74 is reverse and also rotate by
52 -90.
53
55 See "FUNCTIONS" in Math::PlanePath the behaviour common to all path
56 classes.
57 "$path = Math::PlanePath::DekkingCentres->new ()"
59 Create and return a new path object.
60 "($x,$y) = $path->n_to_xy ($n)"
62 Return the X,Y coordinates of point number $n on the path. Points
63 begin at 0 and if "$n < 0" then the return is an empty list.
64 Level Methods
66 "($n_lo, $n_hi) = $path->level_to_n_range($level)"
67 Return "(0, 25**$level - 1)".
68
70 Math::PlanePath, Math::PlanePath::DekkingCurve,
71 Math::PlanePath::CincoCurve, Math::PlanePath::PeanoCurve
72
74 <http://user42.tuxfamily.org/math-planepath/index.html>
75
77 Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 Kevin Ryde
78 This file is part of Math-PlanePath.
80 Math-PlanePath is free software; you can redistribute it and/or modify
82 it under the terms of the GNU General Public License as published by
83 the Free Software Foundation; either version 3, or (at your option) any
84 later version.
85 Math-PlanePath is distributed in the hope that it will be useful, but
87 WITHOUT ANY WARRANTY; without even the implied warranty of
88 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
89 General Public License for more details.
90 You should have received a copy of the GNU General Public License along
92 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
93perl v5.28.0 2017-12-03Math::PlanePath::DekkingCentres(3)