I would like to represent the construction of a house of cards, probably in tikz. Before creating my own, has anyone done anything similar?
3
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Related: Second pentagonal number (OEIS #A005449: Number of cards to build an n-tier house of cards)– Werner ♦Nov 14, 2019 at 23:32
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This doesn't seem like it would take all that much to make a first attempt (probably not as elegant or fun as the given answer, but it would be a first attempt). Is the counting question about 20 stories intended to be a part of the question? @Werner I'm not seeing how the OEIS reference matches with this picture. If you add the bottom three cards, it would seem like this is 3 times a triangular number: 3n(n+1)/2.– TeepeemmNov 15, 2019 at 3:08
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@Teepeemm: For n = 3, 3n(n+1)/2 = 18, while OEIS #A005449's formula of n(3n+1)/2 = 15 in the post.– Werner ♦Nov 15, 2019 at 5:31
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1 Answer
\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[pics/Lam/.style={code={
\draw (-0.45,0.1) -- (0,0.9) -- (0.45,0.1) (-0.45,0) -- (0.45,0);}}]
\path foreach \Y in {1,2,3}
{foreach \X in {1,...,\Y} {(\X-\Y/2,1-\Y) pic{Lam}}};
\end{tikzpicture}
\end{document}
Here is a version (more faithful to the original post) without lines at the bottom and much more. You only need to say
\path pic{card house=3};
See the examples in
\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[pics/Lam/.style={code={
\def\pkv##1{\pgfkeysvalueof{/tikz/Lam/##1}}
\draw (-0.5*\pkv{shrink}*\pkv{width},0.1) --
(0,\pkv{shrink}*\pkv{height}) -- (0.5*\pkv{shrink}*\pkv{width},0.1)
\ifnum#1<\pkv{cutoff} (-0.5*\pkv{shrink}*\pkv{width},0) -- (0.5*\pkv{shrink}*\pkv{width},0)
\fi;}},
pics/card house/.style={code={
\tikzset{Lam/cutoff=#1}
\path foreach \Y in {1,...,#1}
{foreach \X in {1,...,\Y}
{(\X*\pgfkeysvalueof{/tikz/Lam/width}-\Y*\pgfkeysvalueof{/tikz/Lam/width}/2,
-\Y*\pgfkeysvalueof{/tikz/Lam/height}) pic{Lam=\Y}}};
}},
/tikz/Lam/.cd,cutoff/.initial=3,width/.initial=1,height/.initial=1,shrink/.initial=0.9,
]
\path pic{card house=3} (4,0) pic[red]{card house=4} (9,0) pic[blue,thick]{card house=5};
\end{tikzpicture}
\end{document}
What could this be good for? Oh, of course!
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikzlings}
\newif\iftikzling
\begin{document}
\begin{tikzpicture}[pics/Lam/.style={code={
\def\pkv##1{\pgfkeysvalueof{/tikz/Lam/##1}}
\draw (-0.5*\pkv{shrink}*\pkv{width},0.1) --
(0,\pkv{shrink}*\pkv{height}) -- (0.5*\pkv{shrink}*\pkv{width},0.1)
\ifnum#1<\pkv{cutoff} (-0.5*\pkv{shrink}*\pkv{width},0) -- (0.5*\pkv{shrink}*\pkv{width},0)
\fi;
\iftikzling
\tikzling[scale=0.25*\pkv{height}*\pkv{shrink}]
\fi}},
pics/card house/.style={code={
\tikzset{Lam/cutoff=#1}
\path foreach \Y in {1,...,#1}
{foreach \X in {1,...,\Y}
{(\X*\pgfkeysvalueof{/tikz/Lam/width}-\Y*\pgfkeysvalueof{/tikz/Lam/width}/2,
-\Y*\pgfkeysvalueof{/tikz/Lam/height}) pic{Lam=\Y}}};
}},
/tikz/Lam/.cd,cutoff/.initial=3,width/.initial=1,height/.initial=1,shrink/.initial=0.9,
tikzling/.is if=tikzling
]
\path[/tikz/Lam/.cd,height=3,width=3,tikzling=true] pic[blue,thick]{card house=5};
\end{tikzpicture}
\end{document}
