KaTeX Test: The Equations Behind the Zensical Logo¶

This page verifies that KaTeX equation rendering is wired up correctly, using a currency-safe delimiter configuration: plain $ is left alone for prices, and $...$ / $$...$$ are used for math.

Why these three equations¶

Zensical's visual identity — the animated curve on zensical.org — is a strange attractor: a system where simple, deterministic equations produce complex, never-repeating motion. The specific system is the Lorenz attractor, discovered by meteorologist Edward Lorenz while modeling atmospheric convection. It is defined by exactly three coupled ordinary differential equations:

\[ \frac{dx}{dt} = \sigma (y - x) \]

\[ \frac{dy}{dt} = x (\rho - z) - y \]

\[ \frac{dz}{dt} = xy - \beta z \]

With the classic parameters $\sigma = 10$, $\rho = 28$, and $\beta = 8/3$, iterating these three equations produces the butterfly- shaped curve traced by Zensical's logo: small differences in starting conditions lead to wildly different paths, the same "butterfly effect" sensitivity that gave chaos theory its name.

Currency-safe check¶

A KaTeX setup that uses single $...$ for inline math cannot tell the difference between math and a price. This project's configuration (inline_syntax: ['round'] in mkdocs.yml) fixes that: inline math must use $...$, so plain dollar amounts render as plain text.

Migrating this site to Zensical cost the team roughly $0 in new tooling — it's still free and open source.
A hypothetical support plan might run $20 a month, or $1.99 per page — none of that should trigger math rendering.
But the inline equation $e^{i\pi} + 1 = 0$ should render as a proper equation, not literal text.

Display math check¶

\[ \int_0^\infty e^{-x^2}\, dx = \frac{\sqrt{\pi}}{2} \]

If KaTeX is working, the three Lorenz equations above render as typeset math (not raw LaTeX source), the dollar amounts above render as plain text, and the inline Euler's-identity and integral examples render as math.