Synergetic-SQR

Synergetic-SQR is a proof-of-concept 3D renderer that replaces standard Cartesian coordinates with Buckminster Fuller's Synergetic Geometry, a tetrahedral 4D coordinate system. It addresses a fundamental problem in graphics: floating-point error accumulates during rotations, causing geometry to warp over time. By implementing Spread-Quadray Rotors using a Rational Surd field extension, the engine achieves bit-exact rotation—rotating 360 degrees returns objects to their exact starting state.

The system runs algebraic arithmetic natively on GPU shaders, avoiding transcendental approximations entirely. Designed for developers and researchers exploring alternative geometry and numerical stability, it demonstrates ~10x greater topological stability than industry-standard matrix-based approaches in live 60FPS loops. The maker built it with Gemini CLI for pair-programming the core engine.