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The Vortex

The logo on the front page.

2026-03

Tesla’s Vortex might not be the key to understanding the universe, but it is the key to understanding the logo.

Sequence of events

1. I saw this Mathologer video on Tesla’s Vortex.
2. Thought it was cool, played around with it in LaTeX (code below if you want to try).
3. A year later I was pondering a logo and wanted to do something mathematical.
4. Figured out I could make an R and a G from a cardioid curve.
5. Then remembered you can get a cardioid curve with the vortex (the modulus circle), with 2 as the multiplier. And voila!

Process of creation

This is a modulus circle of 91 with multiplier 2.

You can get what looks like an R if you plot from 15 to 60 only.

You can similarly get a G with some finagling.

Decided to use the R only in the end (a double circle is very hard to fit on a rectangular page, as you can see in the image above).

LaTeX code to create the vortex (the modulus circle, if you’re being pedantic). Run it in any LaTeX editor. Overleaf is my favourite.

\documentclass[tikz,border=5mm]{standalone}

\begin{document}
\begin{tikzpicture}
  % Parameters
  \def\modulus{91}
  \def\multiplier{2}
  \def\radius{5}

  \pgfmathtruncatemacro{\last}{\modulus-1}
  % Angle between adjacent points
  \pgfmathsetmacro{\step}{360/\modulus}

  % Circle
  \draw (0,0) circle (\radius);

  \foreach \k in {0,...,\last} {
    % Connect of k-th point
    \pgfmathtruncatemacro{\con}{mod(\multiplier*\k,\modulus)}
    % Angles (90 at the top, going clockwise)
    \pgfmathsetmacro{\angA}{90 - \k*\step}
    \pgfmathsetmacro{\angB}{90 - \con*\step}

    % Chord from k to connect of k
    \draw[line width=0.3pt] (\angA:\radius) -- (\angB:\radius);

    % Labels
    \fill (\angA:\radius) circle (1pt);
    \node[font=\tiny, scale=0.8] at (\angA:\radius+0.3) {\k};
  }
\end{tikzpicture}
\end{document}

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