A “Knead” for Chaos: The Culinary Kneading Process as an Explanatory Metaphor in Chaotic Systems

Before the advent of modern computers, mathematicians used analog circuits to model non-integrable differential equations. This paper investigates the feasibility, functionality, and accuracy of several systems including the solar system, three-body system, and Lorenz attractor. Due to their highly nonlinear nature and circuit limitations, the solar system and three-body systems are not practical to build, with component costs as high as $50,000 and $4,300 respectively. However, the Lorenz attractor can be built and analyzed; even using “economy” components, its output covers the correct attractor. An error analysis concludes that while the Lorenz circuit’s output may have the correct shape, high accuracy components are required for the system to follow the correct trajectory for even just a short period of time. Given these challenges, only a few practical applications of chaotic circuits exist, mainly those that leverage error such as random number generators. Unfortunately, in most other functions, digital computing drastically outperforms analog circuits.