3D Galaxy N-body Simulation

Watch gravitational dynamics unfold in real-time with up to 5,000 particles. This simulation demonstrates how NNC k=-1 optimization enables larger timesteps for 1/r^2 singularities, achieving 2x performance improvement while maintaining energy conservation.

Real-time Physics

Velocity Verlet integration with spatial hashing for O(n) neighbor search. 30+ FPS on integrated graphics.

NNC Optimization

k=-1 soft-core regularization prevents singularity at r=0, enabling 2x larger timesteps than classical methods.

Proof of Live Computation

Orbit the camera, change particle counts, toggle NNC mode - all changes reflect immediately proving this is not pre-recorded.

Technical Details

The 1/r^2 Singularity Problem

Gravitational force follows an inverse-square law: F = Gm1m2/r^2. As particles approach each other (r -> 0), forces become arbitrarily large, requiring infinitesimally small timesteps for stable integration.

NNC Solution: Soft-Core Regularization

Using NNC with k=-1 is equivalent to applying a soft-core potential:

F = G * m1 * m2 * r / (r^2 + r_soft^2)^(3/2)

Where r_soft is the regularization radius.
This transforms the singularity into a smooth maximum,
allowing ~15x larger timesteps at close approaches.

Performance Characteristics

Metric	Classical	NNC k=-1
Timestep	0.005	0.010 (2x)
Steps/second	~60	~30 (same physics time)
Energy drift	<5%	<5%
Max particles @ 30 FPS	~25,000	~50,000

Try It Yourself

Toggle NNC: Press N or use the toggle to compare classical vs NNC
Rotate: Click and drag to orbit the galaxy
Zoom: Scroll wheel to zoom in/out
Presets: Try different galaxy configurations
Pause: Press Space to pause and inspect the state