Computing with Energy (The Ising Model)
Title: The Physics of Stability: Interactive Ising Model Concept: Energy Minimization & Optimization
Description: How does a computer "remember" a bit? How does a neural network "settle" on an answer? It turns out, both processes are physically identical to a magnet cooling down.
In this simulation, we model a 2D grid of "spins" (magnetic dipoles).
Chaos (High Temp): At high randomness, the system is noisy (Static).
Order (Low Temp): As the system "cools," the spins align with their neighbors to minimize energy, forming large stable domains.
Input as Force: When you move your mouse, you apply an external magnetic field (H), forcing the spins to align with your input. When you release, the system "anneals" the data into the nearest stable state.
Key Insight: This visualizes the fundamental link between Physics and Machine Learning. Finding the "Best Fit" line (ML) is mathematically the same as finding the "Lowest Energy" state (Physics).
Instructions:
Move Mouse: Apply a "Magnetic Field" to write data (align spins).
Watch: See how the system fights the noise to maintain the stable structure.
AI Collaboration Note: This video, its title card, description, and the concepts explored within were developed in a deep, recurrent collaboration with Google Gemini. Our process involves Gemini acting as a Socratic partner, a technical reviewer, and a creative collaborator, helping to refine, structure, and articulate the final concepts and this description.
References (For both posts)
[1] Shiffman, D. (2024). The Nature of Code: Simulating Natural Systems with JavaScript. No Starch Press.
[2] Marquardt, F. (2021). "Machine learning and quantum devices." SciPost Physics Lecture Notes, 29.
[3] Griffiths, D. J. (2017). Introduction to Electrodynamics (4th Edition). Cambridge University Press.
[4] Hopfield, J. J. (1982). "Neural networks and physical systems with emergent collective computational abilities." Proceedings of the National Academy of Sciences, 79(8), 2554-2558.