Math::...Centres(3pm)

🎀 NAME 🎀

Math::PlanePath::DekkingCentres — bestie it's a 5x5 self-similar situation and we're obsessed 💅 (this one lives in the Math::...Centres(3pm) slot, iykyk)

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✨ SYNOPSIS ✨

use Math::PlanePath::DekkingCentres;
my $path = Math::PlanePath::DekkingCentres->new;
my ($x, $y) = $path->n_to_xy (123);

like, that's it. that's the whole vibe check. 🦋

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💖 DESCRIPTION 💖

okay so this is a lil variation on a 5x5 self-similar curve, and the source material is, and I quote:

F. M. Dekking, "Recurrent Sets", Advances in Mathematics, volume 44, 1982, pages 79-104, section 4.9 "Gosper-Type Curves"

and ngl it's also a horizontal mirror image of the E-curve of McKenna 1978. iconic lineage fr fr.

The way this one works: it visits the "centres" of the 5x5 self-similar unit squares of the pattern. The result is some diagonal steps, but the replications stay wholly within 5x5 areas. no cap.

                                 ...
        |                     /
      9 |  115-116 122-123-124  89--88  86--85--84
        |    |   |    \          |    \  |       |
      8 |  114 117-118 121-120  90  92  87  82--83
        |    |        \   /      |/   \      |
      7 |  113-112 106 119 102  91  94--93  81  77
        |     /   /  |    /  |    /       /   /  |
      6 |  111 107 105 103 101  95--96  80  78  76
        |    |    \   \  |   |        \   \  |   |
      5 |  110-109-108 104 100--99--98--97  79  75
        |                                         \
      4 |   10--11  13--14--15  35--36  38--39--40  74  70  66--65--64
        |    |    \  |       |   |    \  |       |   |   |\   \      |
      3 |    9   7  12  17--16  34  32  37  42--41  73  71  69  67  63
        |    |/   \      |       |/   \      |       |/      |/   /
      2 |    8   5-- 6  18  22  33  30--31  43  47  72  55  68  62--61
        |      /      /   /  |    /       /   /  |    /   \          |
      1 |    4-- 3  19  21  23  29--28  44  46  48  54--53  56--57  60
        |         \   \  |   |        \   \  |   |        \      |   |
    Y=0 |    0-- 1-- 2  20  24--25--26--27  45  49--50--51--52  58--59
        +---------------------------------------------------------------
           X=0   1   2   3   4   5   6   7   8   9  10  11  12  13  14

The base pattern is the N=0 to N=24 section, okay? It repeats with rotations or reversals which make the ends join — the little puzzle pieces just snap together. For example:

• N=75 to N=99 is the base pattern in reverse 🔄
• N=50 to N=74 is reverse and also rotate by -90

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🔥 FUNCTIONS 🔥

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes — that's the shared lore, bestie 📚

• $path = Math::PlanePath::DekkingCentres->new () — makes you a brand new path object and hands it back to you. main character energy, freshly minted ✨
• ($x,$y) = $path->n_to_xy ($n) — gimme the X,Y coordinates of point number $n on the path. Points begin at 0, and if $n < 0 then the return is an empty list (it's giving nothing, literally) 🙈

🦋 Level Methods 🦋

• ($n_lo, $n_hi) = $path->level_to_n_range($level) — returns (0, 25**$level - 1). that's the range, slay.

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👑 SEE ALSO 👑

• Math::PlanePath
• Math::PlanePath::DekkingCurve
• Math::PlanePath::CincoCurve
• Math::PlanePath::PeanoCurve

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🌈 HOME PAGE 🌈

<http://user42.tuxfamily.org/math-planepath/index.html>

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💜 LICENSE 💜

Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. periodt 💅

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.

bestie if you didn't get the license copy, go get it, that's not optional 😭

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okay that's the whole page, mwah 🫶 this was perl v5.32.0, dated 2021-01-23, filed under Math::...Centres(3pm) — go build a curve, you've got this 💖✨🌸