Welcome to Volume III of The Analyst's Problem: Diagonal Dominance. In this video, we dive deep into the spectral defence simulation I've built to demonstrate how advanced mathematical concepts can entirely replace traditional video game mechanics.
Most games rely on simple Boolean logic and basic subtraction (e.g., Health = Health - Damage). In Diagonal Dominance, we throw that out the window and drive the entire game state using continuous mathematical operators, spectral decomposition, and graph theory.
Here is a breakdown of the unique equations driving the simulation, and how these concepts could revolutionise future game engines:
The Unique Equations Powering the Game:
- Quadratic Form Decomposition
- Projection Operator
- Phase difference
- Constructive interference
The Potential for Gaming Engines:
Why does this matter? Modern physics engines and game state managers are incredibly resource-heavy. By treating a game world as a complex network driven by Spectral Graph Theory and Quadratic Forms, we can simulate highly complex, interconnected environments using lightweight, continuous equations.
Imagine an RPG where a boss's "health" isn't a number, but a matrix of stability that players must mathematically destabilise through specific environmental actions. Or procedural destruction that calculates structural integrity via graph eigenvalues rather than pre-baked physics chunks. This is the future of systemic game design.
If you enjoyed this breakdown, let me know in the comments what mathematical concepts you'd like to see visualised as gameplay next!
Support & Follow The Analyst's Problem:
► Play/Fork the Code on GitHub: https://github.com/jmullings/TheAnalystsProblem
► Subscribe to the Channel: https://www.youtube.com/@TheAnalystsProblem
► Read the E-Book: https://www.amazon.com/s?k="The analyst’s problem"
► Support the Project on Patreon: https://www.patreon.com/posts/jason-mullings-155411204