SPDE-Visuals

This is a preliminary repository and will be improved in the future

A collection of high-quality visuals, illustrations, and figures related to Stochastic Partial Differential Equations (SPDEs). Designed for use in academic posters, presentations, and publications. This repository aims to serve as a resource for researchers, students, and educators in the field of SPDEs and applied mathematics.

Live gallery: https://spdengine.github.io/SPDE-Visuals/

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Table of contents

• Purpose
• Repository contents
• How to use
• How to contribute
• Sample media
• Acknowledgment
• License

Purpose

The purpose of this repository is to provide a comprehensive collection of visuals and examples to aid in the understanding, teaching, and research of Stochastic Partial Differential Equations (SPDEs).

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Repository contents

1. Propagation of the Tall Peaks of the Stochastic Heat Equations:
   • Visualizes the behavior and dynamics of peak propagation in stochastic heat equations.
   • Includes high-resolution images and data files for further exploration.
   • View here.
2. AI-Generated Images for Presentations:
   • Contains AI-generated images that explore abstract and mathematical concepts.
   • Used in academic presentations to highlight key ideas.
   • View here.

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How to use

• Browse the Peak-propogation folder to explore visualizations related to the stochastic heat equation.
• Use the Some_images_by_AI folder for presentation-ready visuals and abstract images.
• Refer to the accompanying references for further context and understanding.

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How to contribute

Contributions of new figures, animations, or small fixes are very welcome.

• Open a pull request or issue briefly describing what you are adding or changing.
• Place new assets in an appropriate folder (Peak-propogation, Some_images_by_AI, or a new subfolder with a short README.md).
• Use descriptive, ASCII-only filenames without spaces (follow patterns such as MJ_*, chenle02_*, Nano_Banana_Pro_*, Sora_*).
• Update the relevant README to include your new material (link + embedded preview) and mention the tool used to generate it (e.g., MidJourney, Gemini 3, Sora@OpenAI).
• Keep file sizes reasonable for GitHub; compress or downscale very large images or videos when possible.
• By contributing, you agree that your additions are compatible with the repository’s CC0 1.0 dedication.

For more contributor details, see AGENTS.md in the repository root.

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Sample media

Videos: stochastic wave equation (Sora@OpenAI)

Short companion videos for the stochastic wave equation “guitar in a sandstorm” example:

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Sample Beamer slide

Here is a sample Beamer slide from a presentation I delivered previously, which incorporated these images: Download PDF

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Acknowledgment

Feel free to use any figures, videos, and other materials from this repository in your talks, lectures, and papers—no formal acknowledgment is required.

If you would like to express gratitude, a brief note such as

Figures inspired by the SPDE-Visuals repository (Le Chen, Auburn University, https://spdengine.github.io/SPDE-Visuals/).

or a link to this GitHub/GitHub Pages project is very much appreciated. For questions or comments, you can reach me at lzc0090@auburn.edu, or visit my webpage: https://webhome.auburn.edu/~lzc0090/index.html.

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License

All materials in this repository are released under the CC0 1.0 Universal public-domain dedication. You may copy, modify, and reuse the contents for any purpose, including commercial use, without asking permission. Where feasible, please avoid implying any endorsement by the author or affiliated institutions.

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