% demo1
\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[scale=2]
\begin{axis}[colormap/viridis]
\addplot3[
	surf,
	samples=18,
	domain=-3:3
]
{exp(-x^2-y^2)*x};
\end{axis}
\end{tikzpicture}
\end{document}

% demo2
\documentclass[tikz]{standalone}
\begin{document}
  \begin{tikzpicture}[domain=0:4]
    \draw[very thin,color=gray] (-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}
\end{document}

% demo3
\documentclass[margin=10pt]{standalone}
\usepackage[siunitx]{circuitikz}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw (0,0)
to[isource, l=$I_0$, v=$V_0$] (0,3)
to[short, -*, i=$I_0$] (2,3)
to[R=$R_1$, i>_=$i_1$] (2,0) -- (0,0);
\draw (2,3) -- (4,3)
to[R=$R_2$, i>_=$i_2$]
(4,0) to[short, -*] (2,0);
\end{tikzpicture}
\end{document}

% demo4
% Poincaré Diagram: Classification of Phase Portraits in the (det A,Tr A)-plane
% Author: Gernot Salzer, 22 Jan 2017
\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{decorations.markings}
\tikzset
 {every pin/.style = {pin edge = {<-}},    % pins are arrows from label to point
  > = stealth,                            % arrow tips look like stealth bombers
  flow/.style =    % everything marked as "flow" will be decorated with an arrow
   {decoration = {markings, mark=at position #1 with {\arrow{>}}},
    postaction = {decorate}
   },
  flow/.default = 0.5,          % default position of the arrow is in the middle
  main/.style = {line width=1pt}                    % thick lines for main graph
 }
% \newtemplate[Scaling, default 0.18]{\NameOfTemplate}{Caption}{Code}
%
% Typesets Code and stores it in the box \NameOfTemplate.
% This way we avoid nested tikzpictures when inserting the templates into the
% main picture, since nesting is not guaranteed to work.
\newcommand\newtemplate[4][0.18]%
 {\newsavebox#2%
  \savebox#2%
   {\begin{tabular}{@{}c@{}}
      \begin{tikzpicture}[scale=#1]
      #4
      \end{tikzpicture}\\[-1ex]
      \templatecaption{#3}\\[-1ex]
    \end{tabular}%
   }%
 }
\newcommand\template[1]{\usebox{#1}}             % use the Code stored in box #1
\newcommand\templatecaption[1]{{\sffamily\scriptsize#1}}       % typeset caption
\newcommand\Tr{\mathop{\mathrm{Tr}}}
\newtemplate\sink{sink}%
 {\foreach \sx in {+,-}                   % for right/left half do:
   {\draw[flow] (\sx4,0) -- (0,0);        %   draw half of horizontal axis
    \draw[flow] (0,\sx4) -- (0,0);        %   draw half of vertical axis
    \foreach \sy in {+,-}                 %   for upper/lower quadrant do:
      \foreach \a/\b in {2/1,3/0.44}      %     draw two half-parabolas
        \draw[flow,domain=\sx\a:0] plot (\x, {\sy\b*\x*\x});
   }
 }
\newtemplate\source{source}%
 {\foreach \sx in {+,-}                   % for right/left half do:
   {\draw[flow] (0,0) -- (\sx4,0);        %   draw half of horizontal axis
    \draw[flow] (0,0) -- (0,\sx4);        %   draw half of vertical axis
    \foreach \sy in {+,-}                 %   for upper/lower quadrant do:
      \foreach \a/\b in {2/1,3/0.44}      %     draw two half-parabolas
        \draw[flow,domain=0:\sx\a] plot (\x, {\sy\b*\x*\x});
   }
 }
\newtemplate\stablefp{line of stable fixed points}%
 {\draw (-4,0) -- (4,0);                  % draw horizontal axis
  \foreach \sy in {+,-}                   % for upper/lower half do:
   {\draw[flow] (0,\sy4) -- (0,0);        %   draw half of vertical axis
    \foreach \x in {-3,-2,-1,1,2,3}       %   draw six vertical half-lines
      \draw[flow] (\x,\sy3) -- (\x,0);
   }
 }
\newtemplate\unstablefp{line of unstable fixed points}%
 {\draw (-4,0) -- (4,0);                  % draw horizontal axis
  \foreach \sy in {+,-}                   % for upper/lower half do:
   {\draw[flow] (0,0) -- (0,\sy4);        %   draw half of vertical axis
    \foreach \x in {-3,-2,-1,1,2,3}       %   draw six vertical half-lines
      \draw[flow] (\x,0) -- (\x,\sy3);
   }
 }
\newtemplate\spiralsink{spiral sink}%
 {\draw (-4,0) -- (4,0);                  % draw horizontal axis
  \draw (0,-4) -- (0,4);                  % draw vertical axis
  \draw [samples=100,smooth,domain=27:7]  % draw spiral
       plot ({\x r}:{0.005*\x*\x});       % Using "flow" here gives "Dimension
  \def\x{26}                              %        too large", so we draw a tiny
  \draw[->] ({\x r}:{0.005*\x*\x}) -- +(0.01,-0.01);%     tangent for the arrow.
 }
\newtemplate\spiralsource{spiral source}%
 {\draw (-4,0) -- (4,0);                  % draw horizontal axis
  \draw (0,-4) -- (0,4);                  % draw vertical axis
  \draw [samples=100,smooth,domain=10:28] % draw spiral
       plot ({-\x r}:{0.005*\x*\x});      % Using "flow" here gives "Dimension
  \def\x{27.5}                            %        too large", so we draw a tiny
  \draw[<-] ({-\x r}:{0.005*\x*\x}) -- +(0.01,-0.008);%   tangent for the arrow.
 }
\newtemplate[0.15]\centre{center}% British spelling since \center is in use
 {\draw (-4,0) -- (4,0);                  % draw horizontal axis
  \draw (0,-4) -- (0,4);                  % draw vertical axis
  \foreach \r in {1,2,3}                  % draw three circles
    \draw[flow=0.63] (\r,0) arc (0:-360:\r cm);
 }
\newtemplate\saddle{saddle}%
 {\foreach \sx in {+,-}                   % for right/left half do:
   {\draw[flow] (\sx4,0) -- (0,0);        %   draw half of horizontal axis
    \draw[flow] (0,0) -- (0,\sx4);        %   draw half of vertical axis
    \foreach \sy in {+,-}                 %   for upper/lower quadrant do:
      \foreach \a/\b/\c/\d in {2.8/0.3/0.7/0.6, 3.9/0.4/1.3/1.1}
        \draw[flow] (\sx\a,\sy\b)         %     draw two bent lines
          .. controls (\sx\c,\sy\d) and (\sx\d,\sy\c)
          .. (\sx\b,\sy\a);
   }
 }
\newtemplate\degensink{degenerate sink}%
 {\draw (0,-4) -- (0,4);                  % draw vertical axis
  \foreach \s in {+,-}                    % for upper/lower half do:
   {\draw[flow] (\s4,0) -- (0,0);         %   draw half of horizontal axis
    \foreach \a/\b/\c/\d in {3.5/4/1.5/1, 2.5/2/1/0.8}
      \draw[flow] (\s-3.5,\s\a)           %   draw two bent lines
        .. controls (\s\b,\s\c) and (\s\b,\s\d)
        .. (0,0);
   }
 }
\newtemplate\degensource{degenerate source}%
 {\draw (0,-4) -- (0,4);                  % draw vertical axis
  \foreach \s in {+,-}                    % for upper/lower half do:
   {\draw[flow] (0,0) -- (\s4,0);         %   draw half of horizontal axis
    \foreach \a/\b/\c/\d in {3.5/4/1.5/1, 2.5/2/1/0.8}
      \draw[flow] (0,0)                   %   draw two bent lines
        .. controls (\s\b,\s\d) and (\s\b,\s\c)
        .. (\s-3.5,\s\a);
   }
 }
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round]
  % MAIN DIAGRAM
  \draw [main,->] (0,-0.3) -- (0,4.7)                            % vertical axis
    node [label={[above]$\scriptstyle\det A$}] {}
    node [label={[above,yshift=0.8cm]%
      {\sffamily\large Poincar\'e Diagram: Classification of Phase
      Portraits in the $(\det A,\Tr A)$-plane}}] {};
  \draw [main,->] (-5,0) -- (5,0)                              % horizontal axis
    node [label={[right,yshift=-0.5ex]$\scriptstyle\Tr A$}] {}; 
  \draw [main, domain=-4:4] plot (\x, {0.25*\x*\x});                % main graph
  \node at (-4,4) [pin={[above]$\scriptstyle\Delta=0$}] {};
  \node at ( 4,4) [pin={[above,align=left]%
    {$\scriptstyle\Delta=0:\;\det A=\frac{1}{4}(\Tr A)^2$}}] {};
  % TEMPLATES describing areas
  \node at ( 0  ,-1.4) {\template\saddle};
  \node at (-4  , 1  ) {\template\sink};
  \node at ( 4  , 1  ) {\template\source}; 
  \node at (-1.8, 3.7) {\template\spiralsink};
  \node at ( 1.8, 3.7) {\template\spiralsource};
  % TEMPLATES labeling lines and points
  \node at ( 0  , 1.2) [pin={[draw,right,xshift=0.3cm]%
    \template\centre}] {};
  \node at (-3  , 0  ) [pin={[draw,below,yshift=-1cm]%
    \template\stablefp}] {};
  \node at ( 3  , 0  ) [pin={[draw,below,yshift=-1cm]%
    \template\unstablefp}] {};
  \node at (-3.5,{0.25*3.5*3.5}) [pin={[draw,left,xshift=-1.15cm,yshift=-0.3cm]%
    \template\degensink}] {};
  \node at ( 3.5,{0.25*3.5*3.5}) [pin={[draw,right,xshift=0.9cm,yshift=-0.3cm]%
    \template\degensource}] {};
  \node at ( 0  , 0  ) [pin={[draw,above left,align=center,xshift=-0.3cm]%
    \templatecaption{uniform}\\[-1ex]\templatecaption{motion}}] {};
\end{tikzpicture}
\end{document}

% demo5
\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}[scale=2]
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=blue] (1) at(0,2){$x_1$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=blue] (2) at(0,0){$x_2$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (3) at(2,-1){$a_3^{(2)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (4) at(2,1){$a_2^{(2)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (5) at(2,3){$a_1^{(2)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (6) at(4,-1){$a_3^{(3)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (7) at(4,1){$a_2^{(3)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=orange] (8) at(4,3){$a_1^{(3)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=purple] (9) at(6,2){$a_1^{(4)}$};
\node[circle,
minimum width =30pt ,
minimum height =30pt ,draw=purple] (10) at(6,0){$a_2^{(4)}$};
\draw[->] (1) --(3);
\draw[->] (1) --(4);
\draw[->] (1) --(5);
\draw[->] (2) --(3);
\draw[->] (2) --(4);
\draw[->] (2) --(5);
\draw[->] (3) --(6);
\draw[->] (3) --(7);
\draw[->] (3) --(8);
\draw[->] (4) --(6);
\draw[->] (4) --(7);
\draw[->] (4) --(8);
\draw[->] (5) --(6);
\draw[->] (5) --(7);
\draw[->] (5) --(8);
\draw[->] (6) --(9);
\draw[->] (6) --(10);
\draw[->] (7) --(9);
\draw[->] (7) --(10);
\draw[->] (8) --(9);
\draw[->] (8) --(10);
\end{tikzpicture}
\end{document}

% demo6
% Author: Till Tantau
% Source: The PGF/TikZ manual
\documentclass[tikz]{standalone}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}[scale=3,cap=round]
% Local definitions
\def\costhirty{0.8660256}
% Colors
\colorlet{anglecolor}{green!50!black}
\colorlet{sincolor}{red}
\colorlet{tancolor}{orange!80!black}
\colorlet{coscolor}{blue}
% Styles
\tikzstyle{axes}=[]
\tikzstyle{important line}=[very thick]
\tikzstyle{information text}=[rounded corners,fill=red!10,inner sep=1ex]
% The graphic
\draw[style=help lines,step=0.5cm] (-1.4,-1.4) grid (1.4,1.4);
\draw (0,0) circle (1cm);
\begin{scope}[style=axes]
    \draw[->] (-1.5,0) -- (1.5,0) node[right] {$x$};
    \draw[->] (0,-1.5) -- (0,1.5) node[above] {$y$};
    \foreach \x/\xtext in {-1, -.5/-\frac{1}{2}, 1}
    \draw[xshift=\x cm] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white]
            {$\xtext$};
    \foreach \y/\ytext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
    \draw[yshift=\y cm] (1pt,0pt) -- (-1pt,0pt) node[left,fill=white]
            {$\ytext$};
\end{scope}
\filldraw[fill=green!20,draw=anglecolor] (0,0) -- (3mm,0pt) arc(0:30:3mm);
\draw (15:2mm) node[anglecolor] {$\alpha$};
\draw[style=important line,sincolor]
    (30:1cm) -- node[left=1pt,fill=white] {$\sin \alpha$} +(0,-.5);
\draw[style=important line,coscolor]
    (0,0) -- node[below=2pt,fill=white] {$\cos \alpha$} (\costhirty,0);
\draw[style=important line,tancolor] (1,0) --
    node [right=1pt,fill=white]
    {
    $\displaystyle \tan \alpha \color{black}=
    \frac{{\color{sincolor}\sin \alpha}}{\color{coscolor}\cos \alpha}$
    } (intersection of 0,0--30:1cm and 1,0--1,1) coordinate (t);
\draw (0,0) -- (t);
\draw[xshift=1.85cm] node [right,text width=6cm,style=information text]
    {
    The {\color{anglecolor} angle $\alpha$} is $30^\circ$ in the
    example ($\pi/6$ in radians). The {\color{sincolor}sine of
        $\alpha$}, which is the height of the red line, is
    \[
    {\color{sincolor} \sin \alpha} = 1/2.
    \]
    By the Theorem of Pythagoras we have ${\color{coscolor}\cos^2 \alpha} +
    {\color{sincolor}\sin^2\alpha} =1$. Thus the length of the blue
    line, which is the {\color{coscolor}cosine of $\alpha$}, must be
    \[
    {\color{coscolor}\cos\alpha} = \sqrt{1 - 1/4} = \textstyle
    \frac{1}{2} \sqrt 3.
    \]%
    This shows that {\color{tancolor}$\tan \alpha$}, which is the
    height of the orange line, is
    \[
    {\color{tancolor}\tan\alpha} = \frac{{\color{sincolor}\sin
        \alpha}}{\color{coscolor}\cos \alpha} = 1/\sqrt 3.
    \]%
    };
\end{tikzpicture}
\end{document}

% demo7
\documentclass[tikz]{standalone}
\usetikzlibrary {angles,calc,quotes}
\begin{document}
\begin{tikzpicture}[angle radius=.75cm, scale=2]
\node (A) at (-2,0)     [red,left]   {$A$};
\node (B) at ( 3,.5)    [red,right]  {$B$};
\node (C) at (-2,2)     [blue,left]  {$C$};
\node (D) at ( 3,2.5)   [blue,right] {$D$};
\node (E) at (60:-5mm)  [below]      {$E$};
\node (F) at (60:3.5cm) [above]      {$F$};
\coordinate (X) at (intersection cs:first line={(A)--(B)}, second line={(E)--(F)});
\coordinate (Y) at (intersection cs:first line={(C)--(D)}, second line={(E)--(F)});
\path
    (A) edge [red, thick]  (B)
    (C) edge [blue, thick] (D)
    (E) edge [thick]       (F)
    pic ["$\alpha$", draw, fill=yellow]   {angle = F--X--A}
    pic ["$\beta$",  draw, fill=green!30] {angle = B--X--F}
    pic ["$\gamma$", draw, fill=yellow]   {angle = E--Y--D}
    pic ["$\delta$", draw, fill=green!30] {angle = C--Y--E};
\node at ($ (D)!.5!(B) $) [right=1cm,text width=6cm,rounded corners,fill=red!20,inner sep=1ex]
    {
    When we assume that $\color{red}AB$ and $\color{blue}CD$ are
    parallel, i.\,e., ${\color{red}AB} \mathbin{\|} \color{blue}CD$,
    then $\alpha = \gamma$ and $\beta = \delta$.
    };
\end{tikzpicture}
\end{document}

% demo8
\documentclass[tikz]{standalone}
\usepackage{chemfig}
\begin{document}
\chemfig{[:-90]HN(-[::-45](-[::-45]R)=[::+45]O)>[::+45]*4(-(=O)-N*5(-(<:(=[::-60]O)-[::+60]OH)-(<[::+0])(<:[::-108])-S>)--)}
\end{document}

\documentclass[tikz]{standalone}
\definecolor{DarkBlue}{rgb}{0,0,0.5} % 添加缺失的颜色定义
\begin{document}
\begin{tikzpicture}[scale=2]
  \node (so32) [align=center] at (-5,-1) {heterotic\\$SO(32)$};
  \node (e8e8) [align=center] at (-3,4) {heterotic\\$E(8) \times E(8)$};
  \node (tiia) [align=center] at (4,3) {Type II A};
  \node (tiib) [align=center] at (5,-2) {Type II B};
  \node (ti) [align=center] at (0,-5) {Type I};
  \draw[bend left,<->] (so32) to node [below right,align=center] {compac-\\tification} (e8e8);
  \draw[bend left,<->] (e8e8) to node [below left] {M-theory} (tiia);
  \draw[bend left,<->] (tiia) to node [below left] {T-duality} (tiib);
  \draw[bend left,<->] (tiib) to node [above left,align=center] {orientifold\\action $\Omega$} (ti);
  \draw[bend left,<->] (ti) to node [above right] {S-duality} (so32);
  \begin{scope}
    % 修正路径绘制方式
    \clip (so32.east) to [bend right] (e8e8.south)
      to [bend right] (tiia.south)
      to [bend right] (tiib.west)
      to [bend right] (ti.north)
      to [bend right] cycle; % 闭合路径
    \foreach \c in {so32.east,e8e8.south,tiia.south,tiib.west,ti.north}{%
        \foreach \r in {1,...,6}{%
            \draw[DarkBlue] (\c) circle (\r*0.15cm); % 使用已定义的颜色
          }
      }
  \end{scope}
  % 修正路径绘制方式
  \draw[bend right,very thick,gray,fill,fill opacity=0.3] 
    (so32.east) to [bend right] (e8e8.south)
    to [bend right] (tiia.south)
    to [bend right] (tiib.west)
    to [bend right] (ti.north)
    to [bend right] cycle; % 闭合路径
  \node (mth) [align=center] at (0,0) {parameter space of\\[2ex]{\Large \textbf{M-Theory}}};
\end{tikzpicture}
\end{document}