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Como completar esta figura usando Tikz?

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Como completar esta figura usando Tikz?

Eu vi a seguinte imagem na Olimpíada de Matemática de Porto Rico. A figura é um tapete que se desdobra.

insira a descrição da imagem aqui

Não consegui fazer a parte do cilindro, não introduzir símbolos nos quadrados pretos

\documentclass{exam}
\usepackage{tikz}           
\usepackage{amsmath}   
\usepackage{amssymb}   
\usepackage{amsfonts}  
\usepackage{latexsym}       %simbolos do Latex    
\usepackage{bbm}        %simbolos de conjuntos   
\usepackage{pstricks}   
\usepackage{pstricks-add, pst-eucl, here}  
\usepackage{MnSymbol}

\begin{document}  
\begin{center}   
\begin{tikzpicture}[scale=0.8, angle=90]

\draw[ultra thick](0,0)--(7,0)--(7,9)--(0,9)--(0,0);    
\draw[thick] (1,0)--(1,9);    
\draw[thick] (2,0)--(2,9);    
\draw[thick] (3,0)--(3,9);   
\draw[thick] (4,0)--(4,9);   
\draw[thick] (5,0)--(5,9);
\draw[thick] (6,0)--(6,9);   
\draw[thick] (7,0)--(7,9);   
\draw[thick] (0,1)--(7,1); 
\draw[thick] (0,2)--(7,2);  
\draw[thick] (0,3)--(7,3);   
\draw[thick] (0,4)--(7,4);   
\draw[thick] (0,5)--(7,5);   
\draw[thick] (0,6)--(7,6);  
\draw[thick] (0,7)--(7,7);  
\draw[thick] (0,8)--(7,8);  
\draw[thick] (0,9)--(7,9);

\draw[thick,<-] (-0.5,0)--(-0.5,4);  
\draw[thick,->] (-0.5,4.5)--(-0.5,9);   
\draw[thick,<-] (0,-0.5)--(2.6,-0.5);  
\draw[thick,->] (3.7,-0.5)--(7,-0.5);

\draw[fill=black] (0,1) rectangle (1,2);  
\draw[fill=black] (2,1) rectangle (3,2);
\draw[fill=black] (4,1) rectangle (5,2);    
\draw[fill=black] (6,1) rectangle (7,2);
\draw[fill=black] (0,3) rectangle (1,4);   
\draw[fill=black] (2,3) rectangle (3,4);  
\draw[fill=black] (4,3) rectangle (5,4);   
\draw[fill=black] (6,3) rectangle (7,4);   
\draw[fill=black] (0,5) rectangle (1,6);    
\draw[fill=black] (2,5) rectangle (3,6);   
\draw[fill=black] (4,5) rectangle (5,6);    
\draw[fill=black] (6,5) rectangle (7,6);    
\draw[fill=black] (0,7) rectangle (1,8);    
\draw[fill=black] (2,7) rectangle (3,8);    
\draw[fill=black] (4,7) rectangle (5,8);    
\draw[fill=black] (6,7) rectangle (7,8);   
\draw[fill=black] (1,6) rectangle (2,7);    
\draw[fill=black] (3,6) rectangle (4,7);   
\draw[fill=black] (5,6) rectangle (6,7);   
\draw[fill=black] (3,0) rectangle (4,1);   
\draw[fill=black] (5,0) rectangle (6,1);   
\draw[fill=black] (1,0) rectangle (2,1);   
\draw[fill=black] (1,2) rectangle (2,3);   
\draw[fill=black] (3,2) rectangle (4,3);   
\draw[fill=black] (5,2) rectangle (6,3);   
\draw[fill=black] (1,4) rectangle (2,5);    
\draw[fill=black] (3,4) rectangle (4,5);   
\draw[fill=black] (5,4) rectangle (6,5);   
\draw[fill=black] (1,8) rectangle (2,9);   
\draw[fill=black] (3,8) rectangle (4,9);
\draw[fill=black] (5,8) rectangle (6,9);

\node at (0.5,0.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (0.5,2.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (0.5,4.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (0.5,6.5) {\LARGE{\textbf{$\ostar$}}}; 
\node at (0.5,8.5) {\LARGE{\textbf{$\ostar$}}};    
\node at (1.5,1.5) {\LARGE{\textbf{$\ostar$}}};    
\node at (1.5,3.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (1.5,5.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (1.5,7.5) {\LARGE{\textbf{$\ostar$}}};    
\node at (2.5,0.5) {\LARGE{\textbf{$\ostar$}}};    
\node at (2.5,2.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (2.5,4.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (2.5,6.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (2.5,8.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (3.5,1.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (3.5,3.5) {\LARGE{\textbf{$\ostar$}}};    
\node at (3.5,5.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (3.5,7.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (4.5,0.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (4.5,2.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (4.5,4.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (4.5,6.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (4.5,8.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (5.5,1.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (5.5,3.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (5.5,5.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (5.5,7.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (6.5,0.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (6.5,2.5) {\LARGE{\textbf{$\ostar$}}}; 
\node at (6.5,4.5) {\LARGE{\textbf{$\ostar$}}}; 
\node at (6.5,6.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (6.5,8.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (6.5,1.5) {\LARGE{\textbf{$\ostar$}}};   
\node at (6.5,3.5) {\LARGE{\textbf{$\ostar$}}};
\node at (6.5,5.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (6.5,7.5) {\LARGE{\textbf{$\ostar$}}};  
\node at (1.5,8.5) {\LARGE{\textbf{$\leftmoon$}}};  
\node at (1.5,5.5) {\LARGE{\textbf{$\leftmoon$}}};  
\node at (3.5,0.5) {\LARGE{\textbf{$\leftmoon$}}}; 
\node at (3.5,2.5) {\LARGE{\textbf{$\leftmoon$}}}; 
\node at (3.5,6.5) {\LARGE{\textbf{$\leftmoon$}}}; 
\node at (5.5,4.5) {\LARGE{\textbf{$\leftmoon$}}};  
\node at (5.5,8.5) {\LARGE{\textbf{$\leftmoon$}}};   
\node at (-0.7, 4.25) {36dm};  
\node at (3.1, -0.5) {36dm}; 
\end{tikzpicture}  
\end{center}    
\end{document}

insira a descrição da imagem aqui

Responder1

Você também pode usar uma matriz para simplificar o código.

\documentclass{exam}
\usepackage{tikz}           
\usepackage{amsmath}   
\usepackage{amsfonts}  
\usepackage{latexsym} 
\usepackage{mathabx} 
\usepackage{MnSymbol}

\usetikzlibrary{shapes.geometric}

\begin{document}  
\begin{center}   
\begin{tikzpicture}[scale=0.8]
  \def\B{\node[fill=black,text=white,minimum width=1cm,minimum height=1cm] {\LARGE$\leftmoon$};}%
  \def\W{\node[fill=white,minimum width=1cm,minimum height=1cm] {\LARGE$\ostar$};}%

\node[matrix,draw=black,ultra thick,inner sep=1pt] (grid)
{
  \W & \B & \W & \B & \W \\
  \B & \W & \B & \W & \B \\
  \W & \B & \W & \B & \W \\
  \B & \W & \B & \W & \B \\
  \W & \B & \W & \B & \W \\
  \B & \W & \B & \W & \B \\
  \W & \B & \W & \B & \W \\
  \B & \W & \B & \W & \B \\
  \W & \B & \W & \B & \W \\
};

\node[xshift=1cm,yshift=-.1cm,cylinder,rotate=90,
  draw=black,thick,fill=gray,
  minimum height=9.35cm,minimum width=2cm] at (grid.east) {};

\end{tikzpicture}  
\end{center}    
\end{document}

imagem de demonstração

Responder2

Tenho que admitir que meu “cilindro” não parece muito realista, mas de qualquer forma, o resultado pode ser alcançado com um código bem mais curto. Se você não entendeu alguma coisa, fique a vontade para perguntar, mas acho que digitarbastantede \nodedefinições fica entediante.

Deixei sua lista de pacotes como estava porque não sei se você os usa em algum outro lugar do seu documento, mas muitos deles não são necessários para este código.

Saída

insira a descrição da imagem aqui

Código

\documentclass[margin=10pt]{standalone}
\usepackage{tikz}           
\usepackage{amsmath}   
\usepackage{amssymb}   
\usepackage{amsfonts}  
\usepackage{latexsym}       %simbolos do Latex    
\usepackage{bbm}        %simbolos de conjuntos   
\usepackage{pstricks}   
\usepackage{pstricks-add, pst-eucl, here}  
\usepackage{MnSymbol}
\usepackage{wasysym}

\usetikzlibrary{arrows.meta, patterns, shadings}

\begin{document}  
\begin{tikzpicture}

\foreach \y [count=\nrow starting from 0] in {0,1,...,9} {
\foreach \x in {0,1,...,7} {
    \pgfmathsetmacro\color{int(mod(\y + \x, 2)) ? "black" : "white"}
    \fill[draw,fill=\color] (\x,\y) rectangle (\x+1,\y+1);
    \ifnum\pdfstrcmp{\color}{white}=0
        \node[font=\bfseries\LARGE] at (\x+.5,\y+.5) {$\ostar$}; 
    \else
        \node[font=\bfseries\LARGE, text=white] at (\x+.5,\y+.5) {$\leftmoon$};
    \fi 
    }
}

\draw[left color=gray!50!black, right color=gray!50!black, middle color=gray!80, pattern color=black] (7.3,.3) --++ (0,9.7) arc (180:0:.7 and .3) -- (8.7,.3) -- cycle;
\fill[gray!30!black] (8,.25) ellipse (.7 and .3);

\draw[{Latex}-{Latex}] (0,-1) -- (8,-1)  node[fill=white, midway] {60dm};
\draw[{Latex}-{Latex}] (-1,0) -- (-1,10) node[fill=white, midway] {36dm};
\end{tikzpicture}    
\end{document}

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