This repository contains a collection of scripts and tools for visualizing elliptic curves mapped onto a torus, particularly over finite fields. The scripts are written in Wolfram Language (Mathematica) and are intended for generating 3D visualizations of elliptic curve points in modular arithmetic.
Elliptic curves are fundamental objects in number theory and cryptography. This project focuses on visualizing these curves over finite fields and mapping them onto the surface of a torus. The visualizations provide insights into the structure of elliptic curves and their properties when working in modular arithmetic.
- Visualization of elliptic curves over finite fields.
- 3D mapping of elliptic curve points onto a torus.
- Support for various parameters including curve coefficients, field size, and iterations.
- Customizable rendering options such as mesh generation and curve thickness.
To use these scripts, you need Wolfram Mathematica installed on your system.
- Clone the repository:
git clone https://github.com/slonweiss/elliptic-curve-visualization.git
- Open the
.wlscripts in Mathematica.
The main script files are structured as follows:
Elliptic-Curve-Loopv2.wl: Handles the core loop for iterating through elliptic curve points and exporting visualizations.Elliptic-Curve-Visualization_Export-*.wl: Multiple versions for experimenting with curve mapping and visual styles.WeierstrassCurvePlot: The primary function used to plot the elliptic curves on a torus.
To generate a visualization, you can execute the provided scripts in Mathematica. For example:
Get["path/to/Elliptic-Curve-Loopv2.wl"]
WeierstrassCurvePlot[iterations, primeModulus]Below is an example of the visualizations produced:
Contributions are welcome! Feel free to submit a pull request or open an issue to discuss improvements.
This project is licensed under the MIT License. See the LICENSE file for details.