What Can You Create with TikZ Code Examples?

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  • Thread starter Thread starter MarkFL
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Discussion Overview

This thread explores various examples of TikZ code that participants can use as templates or inspiration for creating their own images. The discussion includes a range of applications, from geometric shapes to physical models, showcasing the versatility of TikZ in visual representation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant shares a 3D Sudoku cube example using TikZ, emphasizing the importance of not overloading the server with images.
  • Another participant presents an Escher Brick and a Penrose Triangle, discussing the use of macros for defining dimensions and styles in TikZ.
  • A different contribution illustrates the electric dipole moment in a water molecule, highlighting the arrangement of atoms and the dipole vector.
  • Participants also discuss parallel lines and related angles, providing a visual representation of angle relationships under the assumption of parallel lines.
  • One post includes a diagram related to the intersection of lines, with a focus on the axes and important lines in the context of a coordinate system.

Areas of Agreement / Disagreement

There is no explicit consensus or disagreement noted in the discussion, as participants are sharing individual examples without contesting each other's contributions.

Contextual Notes

Some posts include assumptions about the properties of geometric figures and the relationships between angles, but these assumptions are not universally agreed upon or elaborated in detail.

Who May Find This Useful

This discussion may be useful for individuals interested in learning how to create visual representations using TikZ, particularly in the context of mathematics, physics, and engineering.

MarkFL
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I thought it would be nice to begin a thread where we can post examples of TikZ code that the community can use as templates or jumping off points for their own images. I would recommend not posting a huge number of images in the same post, so we don't strain the rendering server (maintained by I like Serena), or MHB's server.

I'll begin with a Sudoku 3D cube:

\begin{tikzpicture}[every node/.style={minimum size=1cm},on grid]
%preamble \usetikzlibrary{positioning}
\begin{scope}[every node/.append style={yslant=-0.5},yslant=-0.5]
\shade[right color=gray!10, left color=black!50] (0,0) rectangle +(3,3);
\node at (0.5,2.5) {9};
\node at (1.5,2.5) {7};
\node at (2.5,2.5) {1};
\node at (0.5,1.5) {2};
\node at (1.5,1.5) {4};
\node at (2.5,1.5) {8};
\node at (0.5,0.5) {5};
\node at (1.5,0.5) {3};
\node at (2.5,0.5) {6};
\draw (0,0) grid (3,3);
\end{scope}
\begin{scope}[every node/.append style={yslant=0.5},yslant=0.5]
\shade[right color=gray!70,left color=gray!10] (3,-3) rectangle +(3,3);
\node at (3.5,-0.5) {3};
\node at (4.5,-0.5) {9};
\node at (5.5,-0.5) {7};
\node at (3.5,-1.5) {6};
\node at (4.5,-1.5) {1};
\node at (5.5,-1.5) {5};
\node at (3.5,-2.5) {8};
\node at (4.5,-2.5) {2};
\node at (5.5,-2.5) {4};
\draw (3,-3) grid (6,0);
\end{scope}
\begin{scope}[every node/.append style={
yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
]
\shade[bottom color=gray!10, top color=black!80] (6,3) rectangle +(-3,-3);
\node at (3.5,2.5) {1};
\node at (3.5,1.5) {4};
\node at (3.5,0.5) {7};
\node at (4.5,2.5) {5};
\node at (4.5,1.5) {6};
\node at (4.5,0.5) {8};
\node at (5.5,2.5) {2};
\node at (5.5,1.5) {3};
\node at (5.5,0.5) {9};
\draw (3,0) grid (6,3);
\end{scope}
\end{tikzpicture}

And a belt and pulley system:

\begin{tikzpicture}

% Definitions
\pgfmathsetmacro{\b}{75}
\pgfmathsetmacro{\a}{15}
\pgfmathsetmacro{\R}{2}
\pgfmathsetmacro{\r}{1}
\pgfmathsetmacro{\P}{\R*tan(\b)}
\pgfmathsetmacro{\Q}{\R/cos(\b)}
\pgfmathsetmacro{\p}{\r/tan(\a)}
\pgfmathsetmacro{\q}{\r/sin(\a)}

% Pulleys

% Big pulley
\draw (0,0) circle (\R) ;
\fill[left color=gray!80, right color=gray!60, middle
color=white] (0,0) circle (\R) ;
\draw[thick, white] (0,0) circle (.8*\R);
\shade[ball color=white] (0,0) circle (.3) node[left,xshift=-5] {$P$};

% small pulley
\draw (\Q+\q-.3, 0) circle (\r);
\fill[left color=gray!80, right color=gray!60, middle
color=white] (\Q+\q-.3, 0) circle (\r) ;
\draw[thick, white] (\Q+\q-.3,0) circle (.8*\r);
\shade[ball color=white] (\Q+\q-.3,0) circle (.15)
node[right, xshift=2] {$Q$};

% belt and point labels
\begin{scope}[ultra thick]
\draw (\b:\R) arc (\b:360-\b:\R) ;
\draw (\b:\R) -- ( \P, 0 );
\draw (-\b:\R) -- ( \P, 0 );
\draw (\Q-.3,0) -- + (\a:\p) arc (105:-105:\r) ;
\draw (\Q-.3,0) -- + (-\a:\p);
%\draw (\b:\R) arc (\b:360-\b:\r) ;
\end{scope}

\draw (0,0) -- (\b:\R) node[midway, above,sloped] {$R$} node[above] {$A$};
\draw (-\b:\R)--(0,0) ;
\draw (\Q+\q-.3,0) -- +(105:\r) node[midway,above, sloped] {$r$}
node[above] {$E$};
\draw (\Q+\q-.3,0) -- +(-105:\r) node[below] {$D$};
\node[below] at (-\b:\R) {$B$};
\node[below] at (\Q-.3,0) {$C$};

% center line
\draw[dash pattern=on5pt off3pt] (0,0) -- (\Q+\q-.3,0);

% angle label
\node[fill=white] at (0.73*\Q, 0) {$\theta$} ;
\draw (\Q-1.8,0) arc (180:195:1.5);
\draw (\Q-1.8,0) arc (180:165:1.5);
\end{tikzpicture}
 
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Escher Brick:

\begin{tikzpicture}[scale=4.5, line join=bevel]
% \a and \b are two macros defining characteristic
% dimensions of the impossible brick.
\pgfmathsetmacro{\a}{0.18}
\pgfmathsetmacro{\b}{1.37}

\tikzset{%
apply style/.code={\tikzset{#1}},
brick_edges/.style={thick,draw=black},
face_coloura/.style={fill=gray!50},
face_colourb/.style={fill=gray!25},
face_colourc/.style={fill=gray!90},
}

\foreach \theta/\v/\facestyleone/\facestyletwo in {%
0/0/{brick_edges,face_coloura}/{brick_edges,face_colourc},
180/-\a/{brick_edges,face_colourb}/{brick_edges,face_colourc}
}{
\begin{scope}[rotate=\theta,shift={(\v,0)}]
\draw[apply style/.expand once=\facestyleone]
({-.5*\b},{1.5*\a}) --
++(\b,0) --
++(-\a,-\a) --
++({-\b+2*\a},0) --
++(0,-{2*\a}) --
++(\b,0) --
++(-\a,-\a) --
++(-\b,0) --
cycle;
\draw[apply style/.expand once=\facestyletwo]
({.5*\b},{1.5*\a}) --
++(0,{-2*\a}) --
++(-\a,0) --
++(0,\a) --
cycle;
\end{scope}
}
\end{tikzpicture}

Penrose Triangle:

\begin{tikzpicture}[scale=1, line join=bevel]

% \a and \b are two macros defining characteristic
% dimensions of the Penrose triangle.
\pgfmathsetmacro{\a}{2.5}
\pgfmathsetmacro{\b}{0.9}

\tikzset{%
apply style/.code = {\tikzset{#1}},
triangle_edges/.style = {thick,draw=black}
}

\foreach \theta/\facestyle in {%
0/{triangle_edges, fill = gray!50},
120/{triangle_edges, fill = gray!25},
240/{triangle_edges, fill = gray!90}%
}{
\begin{scope}[rotate=\theta]
\draw[apply style/.expand once=\facestyle]
({-sqrt(3)/2*\a},{-0.5*\a}) --
++(-\b,0) --
({0.5*\b},{\a+3*sqrt(3)/2*\b}) -- % higher point
({sqrt(3)/2*\a+2.5*\b},{-.5*\a-sqrt(3)/2*\b}) -- % rightmost point
++({-.5*\b},-{sqrt(3)/2*\b}) -- % lower point
({0.5*\b},{\a+sqrt(3)/2*\b}) --
cycle;
\end{scope}
}
\end{tikzpicture}
 
The electric dipole moment (p) in the water molecule

\begin{tikzpicture}[>=latex,scale=1.3]
\shade[ball color=gray!10!] (0,0) coordinate(Hp) circle (.9) ;
\shade[ball color=gray!10!] (2,-1.53) coordinate(O) circle (1.62) ;
\shade[ball color=gray!10!] (4,0) coordinate(Hm) circle (.9) ;
\draw[thick,dashed] (0,0) -- (2,-1.53) -- (4,0) ;
\draw[thick] (2,.2) -- (2,1.5) node
{$\mathbf{p}$} ;
\draw (2.48,-1.2) arc (33:142:.6) ;
\draw (2,-.95) node[above]{$105^{\circ}$} ;
\draw (0,.2) node
{H$^+$} ;
\draw (4,.2) node
{H$^-$} ;
\draw (2,-1.63) node[below]{O$^{2-}$} ;
\foreach \point in {O,Hp,Hm}
\fill [black] (\point) circle (2pt) ;
\end{tikzpicture}​
 
Parallel lines and related angles

\begin{tikzpicture}
\draw[fill=yellow] (0,0) -- (60:.75cm) arc (60:180:.75cm);
\draw(120:0.4cm) node {$\alpha$};

\draw[fill=green!30] (0,0) -- (right:.75cm) arc (0:60:.75cm);
\draw(30:0.5cm) node {$\beta$};

\begin{scope}[shift={(60:2cm)}]
\draw[fill=green!30] (0,0) -- (180:.75cm) arc (180:240:.75cm);
\draw (30:-0.5cm) node {$\gamma$};

\draw[fill=yellow] (0,0) -- (240:.75cm) arc (240:360:.75cm);
\draw (-60:0.4cm) node {$\delta$};
\end{scope}

\begin{scope}[thick]
\draw (60:-1cm) node[fill=white] {$E$} -- (60:3cm) node[fill=white] {$F$};
\draw[red] (-2,0) node
{$A$} -- (3,0)
node
{$B$};
\draw[blue,shift={(60:2cm)}] (-3,0) node
{$C$} -- (2,0)
node
{$D$};
\draw[shift={(60:1cm)},xshift=4cm]
node [right,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 $\alpha = \delta$ and $\beta = \gamma$.
};
\end{scope}
\end{tikzpicture}

Intersection of

\begin{tikzpicture}
%preamble \usetikzlibrary{arrows}
[
scale=5,
axis/.style={very thick, ->, >=stealth'},
important line/.style={thick},
dashed line/.style={dashed, thin},
pile/.style={thick, ->, >=stealth', shorten <=2pt, shorten
>=2pt},
every node/.style={color=black}
]
% axis
\draw[axis] (-0.1,0) -- (1.1,0) node(xline)

{$G\uparrow/T\downarrow$};
\draw[axis] (0,-0.1) -- (0,1.1) node(yline)[above] {$E$};
% Lines
\draw[important line] (.15,.15) coordinate (A) -- (.85,.85)
coordinate (B) node[right, text width=5em] {$Y^O$};
\draw[important line] (.15,.85) coordinate (C) -- (.85,.15)
coordinate (D) node[right, text width=5em] {$\mathit{NX}=x$};
% Intersection of lines
\fill[red] (intersection cs:
first line={(A) -- (B)},
second line={(C) -- (D)}) coordinate (E) circle (.4pt)
node[above,] {$A$};
% The E point is placed more or less randomly
\fill[red] (E) +(-.075cm,-.2cm) coordinate (out) circle (.4pt)
node[below left] {$B$};
% Line connecting out and ext balances
\draw [pile] (out) -- (intersection of A--B and out--[shift={(0:1pt)}]out)
coordinate (extbal);
\fill[red] (extbal) circle (.4pt) node[above] {$C$};
% line connecting out and int balances
\draw [pile] (out) -- (intersection of C--D and out--[shift={(0:1pt)}]out)
coordinate (intbal);
\fill[red] (intbal) circle (.4pt) node[above] {$D$};
% line between out og all balanced out :)
\draw[pile] (out) -- (E);
\end{tikzpicture}

Intersecting lines

\begin{tikzpicture}[scale=1.5]
% Draw axes
\draw [<->,thick] (0,2) node (yaxis) [above] {$y$}
|- (3,0) node (xaxis)
{$x$};
% Draw two intersecting lines
\draw (0,0) coordinate (a_1) -- (2,1.8) coordinate (a_2);
\draw (0,1.5) coordinate (b_1) -- (2.5,0) coordinate (b_2);
% Calculate the intersection of the lines a_1 -- a_2 and b_1 -- b_2
% and store the coordinate in c.
\coordinate (c) at (intersection of a_1--a_2 and b_1--b_2);
% Draw lines indicating intersection with y and x axis. Here we use
% the perpendicular coordinate system
\draw[dashed] (yaxis |- c) node
{$y'$}
-| (xaxis -| c) node[below] {$x'$};
% Draw a dot to indicate intersection point
\fill[red] (c) circle (2pt);
\end{tikzpicture}​
 
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