\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes,calendar,matrix,backgrounds,folding}




\begin{document}

\pagestyle{empty}



% Math engine
\pgfmathsetseed{1}
\begin{tikzpicture}[x=5pt,y=5pt,thick,baseline,cap=round]
    \coordinate (current point) at (0,0);
    \coordinate (old velocity) at (0,0);
    \coordinate (new velocity) at (rand,rand);
    \foreach \i in {0,1,...,100}
    {
        \draw[black!\i] (current point)
        .. controls ++([scale=-1]old velocity) and
            ++(new velocity) .. ++(rand,rand)
            coordinate (current point);
        \coordinate (old velocity) at (new velocity);
        \coordinate (new velocity) at (rand,rand);
    };
\end{tikzpicture}

% Inline plotting
\begin{tikzpicture}[domain=0:4,scale=0.5]
    \draw[very thin,color=black!20] (-0.1,-1.1) grid (3.9,3.9);
    \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
    \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
    \draw[color=red] plot (\x,\x) node[right] {$f(x) =x$};
    \draw[color=blue] plot (\x,{sin(\x r)}) node[right] {$f(x) = \sin x$};
    \draw[color=orange] plot (\x,{0.05*exp(\x)})
        node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
\end{tikzpicture}

% New node shapes
\begin{tikzpicture}
    \matrix[nodes={draw, thick, fill=blue!20,minimum size=1cm},
        row sep=0.3cm,column sep=0.5cm] {
    \node[regular polygon,regular polygon sides=5] {};&
    \node[regular polygon,regular polygon sides=7] {};&
    \node[regular polygon,regular polygon sides=9] {};\\
    \node[star,star points=4] {};&
    \node[star,star points=7,star point ratio=0.8] {};&
    \node[star,star points=10] {};\\
    };
\end{tikzpicture}

% Calendar library
\begin{tikzpicture}
    \calendar [ dates=2007-07-01 to 2007-07-last,
               week list,inner sep=2pt,month label above centered,
               month text=\%mt \%y0
        ]
    if (weekend) [red,nodes={draw=none}];
\end{tikzpicture}


% Matrices
\begin{tikzpicture}[>=stealth,->,shorten >=2pt,looseness=.5,auto]
    \matrix [matrix of math nodes,
        column sep={2cm,between origins},
        row sep={3cm,between origins},
        nodes={circle, draw, minimum size=7.5mm}]
        {
            & |(A)| A & \\
            |(B)| B & |(E)| E & |(C)| C \\
            & |(D)| D \\
        };
    \tikzstyle{every node}=[font=\small\itshape]
    \draw (A) to [bend left] (B) node [midway] {g};
    \draw (B) to [bend left] (A) node [midway] {f};
    \draw (D) -- (B) node [midway] {c};
    \draw (E) -- (B) node [midway] {b};
    \draw (E) -- (C) node [near end] {a};
    \draw [-,line width=8pt,draw=white]
        (D) to [bend right, looseness=1] (A);
    \draw (D) to [bend right, looseness=1] (A)
        node [near start] {b} node [near end] {e};
\end{tikzpicture}

% Paper folding library
\begin{tikzpicture}[transform shape]
\tikzfoldingdodecahedron
    [folding line length=6mm,
    face 1={ \node[red] {1};},
    face 2={ \node {2};},
    face 3={ \node {3};},
    face 4={ \node {4};},
    face 5={ \node {5};},
    face 6={ \node {6};},
    face 7={ \node {7};},
    face 8={ \node {8};},
    face 9={ \node {9};},
    face 10={\node {10};},
    face 11={\node {11};},
    face 12={\node {12};}];
\end{tikzpicture}

\end{document}

