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\RequirePackage{xcolor}
\definecolor{diverging4-1-1}{RGB}{44,123,182}
\definecolor{diverging4-1-2}{RGB}{171,217,233}
\definecolor{diverging4-1-3}{RGB}{253,174,97}
\definecolor{diverging4-1-4}{RGB}{215,25,28}
\definecolor{diverging4-2-1}{RGB}{94,60,153}
\definecolor{diverging4-2-2}{RGB}{178,171,210}
\definecolor{diverging4-2-3}{RGB}{253,184,99}
\definecolor{diverging4-2-4}{RGB}{230,97,1}
\definecolor{sequential4-1}{RGB}{34,94,168}
\definecolor{sequential4-2}{RGB}{65,182,196}
\definecolor{sequential4-3}{RGB}{161,218,180}
\definecolor{sequential4-4}{RGB}{235,235,184}
\definecolor{sequential4-1-1}{RGB}{34,94,168}
\definecolor{sequential4-1-2}{RGB}{65,182,196}
\definecolor{sequential4-1-3}{RGB}{161,218,180}
\definecolor{sequential4-1-4}{RGB}{235,235,184}
\definecolor{qualitative4-1}{RGB}{51,160,44}
\definecolor{qualitative4-2}{RGB}{178,223,138}
\definecolor{qualitative4-3}{RGB}{31,120,180}
\definecolor{qualitative4-4}{RGB}{166,206,227}
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% square lattice (width #1, height #2, origin #3, spacing #4)
\def\grid#1#2#3{
\foreach\i in {0,...,#2}{
\draw#3++(0,\i)--++(#1,0);
}
\foreach\i in {0,...,#1}{
\draw#3++(\i,0)--++(0,#2);
}
}
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\def\gridcolor#1#2#3#4{
\foreach\i in {0,...,#2}{
\draw[color=#4]#3++(0,\i)--++(#1,0);
}
\foreach\i in {0,...,#1}{
\draw[color=#4]#3++(\i,0)--++(0,#2);
}
}
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% 3-staircase (color #1, position #2)
% speedup
\def\staircase#1#2{
\fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
\draw[color=white]#2++(-0.5,0)--++(3,0);
\draw[color=white]#2++(-0.5,1)--++(2,0);
\draw[color=white]#2++(-0.5,2)--++(1,0);
\draw[color=white]#2++(0,-0.5)--++(0,3);
\draw[color=white]#2++(1,-0.5)--++(0,2);
\draw[color=white]#2++(2,-0.5)--++(0,1);
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\draw[color=black, line width=2pt]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
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}
%\def\staircase#1#2{
% \fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
% \begin{scope}
% \clip#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
% \grid44{[color=white]#2++(-1,-1)}
% \end{scope}
% \draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
%}
% 4-staircase (color #1, position #2)
\def\Staircase#1#2{
\fill[color=#1]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
\begin{scope}
\clip#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
\grid55{[color=white]#2++(-1,-1)}
\end{scope}
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\draw[color=black, line width=2pt]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
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}
% 5-staircase (color #1, position #2)
\def\staircaseV#1#2{
\fill[color=#1]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
\begin{scope}
\clip#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
\grid55{[color=white]#2++(-1,-1)}
\end{scope}
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\draw[color=black, line width=2pt]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
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}
% square (color #1, position #2)
\def\square#1#2{
\fill[color=#1]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
\begin{scope}
\clip#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
\grid22{[color=white]#2++(-1,-1)}
\end{scope}
%\draw[color=black]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
}
% disk (color #1, position #2)
\def\disk#1#2{
\fill[color=#1]#2circle(2.5);
\begin{scope}
\clip#2circle(2.5);
\grid66{[color=white]#2++(-3,-3)}
\end{scope}
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\draw[color=black, line width=2pt]#2circle(2.5);
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}
% octagon (color #1, position #2)
\def\octagon#1#2{
\fill[color=#1]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
\begin{scope}
\clip#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
\grid66{[color=white]#2++(-3,-3)}
\end{scope}
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\draw[color=black, line width=2pt]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
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}