Topic Visualizers

Interactive web demonstrations and other visualizations built by Theodore P. Pavlic covering a range of topics in science, mathematics, statistics, and engineering.

Live site: https://tpavlic.github.io/topic_visualizers/

Each visualization is a self-contained HTML page that works standalone or can be embedded in course management systems (e.g., Canvas LMS) as an iframe.

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Contents

Nonlinear Systems

Demo	Description
jacobian_linearization/	See how nullclines locate equilibria, what the Jacobian linearization reveals about their stability, and what the nullcline geometry can and cannot show on its own.
lyapunov_functions/	Explore Lyapunov functions and level-set curves for common nonlinear dynamical systems, then synthesize them automatically with sum-of-squares programming that exports runnable MATLAB and Python code.
chaos/	Explore multi-scroll chaotic attractors and hyperchaos, and how their dynamics underpin image-encryption schemes.

Statistics

Demo	Description
survival_analysis/	Explore exponential transition rates, right censoring, and repeated events through interactive survival curves and two-state transition models.
glmm_analyzer/	Load a table, choose a family and link, fit a generalized linear model with or without a random effect, check its residuals, plot its predictions, see how much of the variance it explains, compare candidate models by AIC, and regenerate every result in R, Python, or MATLAB.

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Adding a new visualization

Each visualization lives in its own subdirectory:

my_demo/
  my_demo.html          # self-contained page
  my_demo-preview.png   # preview image for OG/Twitter cards

For a new my_demo.html, the checklist is:

1. <head> metadata:

   • Include <title>, <meta name="description">, and the full Open Graph + Twitter card block (see any existing demo for the template)
   • Use the preview image as og:image and twitter:image; set width/height accurately
   • For Twitter/X, the image should be close to 2:1 aspect ratio and under 5 MB

2. Back-link footer – add at the bottom of <body>:

   <footer id="back-link-footer" style="max-width:CONTENT_MAX_WIDTH;margin:0 auto;padding:0 CONTENT_HPAD 1.5rem;">
     <div style="padding-top:0.75rem;border-top:1px solid #e0e0e0;font-size:0.8rem;color:#888;">
       <a href="../" style="color:#2e7d32;text-decoration:none;" onmouseover="this.style.textDecoration='underline'" onmouseout="this.style.textDecoration='none'">&larr; All visualizations</a>
     </div>
   </footer>
   <script>
   if (window.self !== window.top) { var f = document.getElementById('back-link-footer'); if (f) f.style.display = 'none'; }
   </script>

   Set CONTENT_MAX_WIDTH and CONTENT_HPAD to the max-width and horizontal padding of the page's main centered content container, so the back-link and its rule align with the page content (the border-top lives on the inner <div>, inside the padding, so its length matches the main footer's rule). The script hides the footer when the page is embedded in a Canvas iframe.

3. Index entry – add a <li> to the appropriate <section> in index.html, following the existing pattern (thumbnail + title + one-sentence description). Create a new <section class="demo-section"> block if no suitable section exists yet.

4. README entry – add a row to the appropriate table under ## Contents.

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See also

Other projects by the same author that visitors here may find complementary:

• Research Sandbox – work-in-progress interactive demonstrations meant for communication and exploration of ideas related to ongoing research projects.
• Bio-Inspired AI & Optimization – Course Visualizations – supplemental interactive explorers for IEE/CSE 598: Bio-Inspired AI and Optimization at Arizona State University, spanning genetic algorithms, swarm intelligence, neural networks, and other bio-inspired methods.
• Simulating Stochastic Systems – Course Visualizations – supplemental interactive explorers for IEE 475: Simulating Stochastic Systems at Arizona State University, spanning pseudorandom number generation, input modeling, output analysis, confidence intervals, statistical power, and comparison of alternative systems.
• Notes, Documents, & Guides – Markdown-formatted notes and instructional guides on a variety of fundamental and applied science and engineering topics.
• Lectures and short video tutorials on YouTube, including the Office Hours playlist.

License

Released under the MIT License. Copyright © 2026 Theodore P. Pavlic.