├── .gitignore ├── wheels.pdf ├── images ├── wheels-0.png ├── wheels-1.png ├── wheels-2.png ├── wheels-3.png ├── wheels-4.png ├── wheels-5.png ├── wheels-6.png ├── wheels-7.png ├── wheels-8.png ├── wheels-9.png ├── wheels-10.png └── wheels-11.png ├── LICENSE ├── wheels.tex └── README.md /.gitignore: -------------------------------------------------------------------------------- 1 | *.aux 2 | *.log 3 | -------------------------------------------------------------------------------- /wheels.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/wheels.pdf -------------------------------------------------------------------------------- /images/wheels-0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-0.png -------------------------------------------------------------------------------- /images/wheels-1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-1.png -------------------------------------------------------------------------------- /images/wheels-2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-2.png -------------------------------------------------------------------------------- /images/wheels-3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-3.png -------------------------------------------------------------------------------- /images/wheels-4.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-4.png -------------------------------------------------------------------------------- /images/wheels-5.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-5.png -------------------------------------------------------------------------------- /images/wheels-6.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-6.png -------------------------------------------------------------------------------- /images/wheels-7.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-7.png -------------------------------------------------------------------------------- /images/wheels-8.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-8.png -------------------------------------------------------------------------------- /images/wheels-9.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-9.png -------------------------------------------------------------------------------- /images/wheels-10.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-10.png -------------------------------------------------------------------------------- /images/wheels-11.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alexwlchan/lorenz-wheels/main/images/wheels-11.png -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Copyright (c) 2022 Alex Chan 2 | 3 | Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: 4 | 5 | The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 6 | 7 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 8 | -------------------------------------------------------------------------------- /wheels.tex: -------------------------------------------------------------------------------- 1 | \documentclass[tikz, 18pt]{standalone} 2 | 3 | \definecolor{DarkBlue}{HTML}{201db9} 4 | \definecolor{DarkGreen}{HTML}{19a323} 5 | \definecolor{DarkRed}{HTML}{C7301F} 6 | 7 | \newcommand\drawWheel[3]{ 8 | \begin{tikzpicture} 9 | %\fill [white] (0, 0) circle (6); 10 | \draw [#1, line width=1.5pt] (0, 0) circle (1); 11 | \foreach \s in {1, ..., #2} { 12 | \draw [#1, line width=1.5pt] (90+360/#2*\s:1) -- (90+360/#2*\s:1.15); 13 | } 14 | \node [#1] at (0, 0) {\huge{#3}}; 15 | \end{tikzpicture} 16 | } 17 | 18 | \begin{document} 19 | \drawWheel{DarkBlue}{43}{$\psi_1$} 20 | \drawWheel{DarkBlue}{47}{$\psi_2$} 21 | \drawWheel{DarkBlue}{51}{$\psi_3$} 22 | \drawWheel{DarkBlue}{53}{$\psi_4$} 23 | \drawWheel{DarkBlue}{59}{$\psi_5$} 24 | 25 | \drawWheel{DarkGreen}{41}{$\chi_1$} 26 | \drawWheel{DarkGreen}{31}{$\chi_2$} 27 | \drawWheel{DarkGreen}{29}{$\chi_3$} 28 | \drawWheel{DarkGreen}{26}{$\chi_4$} 29 | \drawWheel{DarkGreen}{23}{$\chi_5$} 30 | 31 | \drawWheel{DarkRed}{37}{$\mu_1$} 32 | \drawWheel{DarkRed}{61}{$\mu_2$} 33 | \end{document} 34 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # lorenz-wheels 2 | 3 | This is some TikZ code I made to illustrate the wheels of a [Lorenz cipher machine], which was used by the German Army during World War II. 4 | 5 | The machine had twelve wheels, each with a different number of "cams" (switches), and they were grouped into three sets by the British codebreakers: psi/ψ, chi/χ, and mu/μ wheels. 6 | 7 | 8 | 9 | 12 | 15 | 18 | 19 |
10 | 11 | 13 | 14 | 16 | 17 |
20 | 21 | The diagrams are drawn using [TikZ], a library for creating graphics in LaTeX. 22 | The ability to draw points using polar coordinates made it quite pleasant. 23 | 24 | I never used the illustrations, but I kept the code as a useful example of how to do diagrams in TikZ that I could get into other places. 25 | 26 | [Lorenz cipher machine]: https://en.wikipedia.org/wiki/Lorenz_cipher 27 | [TikZ]: https://tikz.dev/ 28 | 29 | ## To create the illustrations 30 | 31 | To render as PDF: 32 | 33 | ``` 34 | $ pdflatex wheels.tex 35 | ``` 36 | 37 | To convert the PDF to a series of PNG images with transparent backgrounds, use ImageMagick: 38 | 39 | ``` 40 | $ convert -background none -density 500 wheels.pdf images/wheels.png 41 | ``` 42 | 43 | ## Further reading 44 | 45 | - [Illustrating the cipher wheels of a Lorenz machine](https://alexwlchan.net/2022/04/lorenz-wheels/), a blog post I wrote that gives a bit more context and background 46 | - [Tony Sale's website](https://www.codesandciphers.co.uk/virtualbp/fish/fishindex.htm), which explains the Lorenz cipher and the British codebreaking response in more detail 47 | --------------------------------------------------------------------------------