McAi / Physics lab
Nine simulations where every position falls out of an integrator, not a tween: a Valheim-style wall that loses its footing block by block, comets bent by Newton's exact 1/r² law, twelve pendulums drifting into a wave, and Diablo-style isometric scenes where a hero displaces water, flattens grass and bursts a chest. Each frame is path-traced offline to a looping GIF - pure C#, no game engine.
Destruction and gravity
Rigid-body impulse, structural cascade, and three-body Newtonian gravity - integrated, then rendered.
Rigid-body impulse
A 4 kg ball fires into a wall of unit-mass blocks. Each block is an immutable Body integrated under uniform gravity and linear drag; the strike transfers a normal impulse (restitution e = 0.45) and the stack collapses.
Structural cascade
Every block tracks its mass, health and which neighbours hold it up. Knock out a supporter and the block loses its footing and drops as a free body under gravity. Five cannonballs fire on staggered timers and the wall cascades into a ragdoll of debris.
Orbital mechanics
A 1-unit comet on a hyperbolic flyby past a 350-mass planet, driven by Newton's exact 1/r² attraction (Forces.NewtonGravity, G = 20). The ghost trail traces the true conic arc; the tiny recoil is booked back onto the planet, so momentum stays conserved.
Nonlinear dynamics
Twelve pendulums with lengths tuned so pendulum k runs (10 + k) swings in 12 s, all released together. Each is the full nonlinear ODE theta″ = -(g/L) sin theta, stepped by RK4 - no small-angle cheat - so the travelling, standing and burst patterns are genuine phase drift.
N-body gravity
A 20-body cluster on circular orbits around a 30-mass core is torn into a tidal stream when a 600-mass perturber sweeps by. Every pair feels Newtonian gravity, so near-side particles are pulled harder than far-side and the cluster elongates.
Diablo-style / isometric
A 45° isometric camera over four game moments where the world reacts to the hero - displacement, springs, impulse and a wave PDE.
Fluid displacement
The hero pushes through a ParticlePool: the body volume shoves particles aside into a bow wave, splash and a trailing wake. Every droplet position comes out of the integrator.
Damped springs
Each blade is a damped torsional spring solved as its own ODE, driven by SimplexNoise2D wind and a radial shove from the passing hero, then springing back to vertical once he clears.
Impulse and restitution
A chest bursts and fans items out on a velocity spread. Each piece falls under gravity and bounces with its own restitution - impulse law j = -(1 + e) · v_rel · n / (1/m_a + 1/m_b) - until it comes to rest.
Wave equation
A genuine 2D wave PDE ∂²h/∂t² = c²∇²h on a finite-difference grid, sub-stepped to honour the CFL condition, with reflective (Neumann) walls so the hero's footstep ripples bounce off the pool edges and interfere.
How it works
Each scene runs a small solver every frame - a Body under Forces.UniformGravity and Forces.LinearDrag, Newtonian NewtonGravity between bodies, an Rk4Step pendulum, a finite-difference wave field - then hands the resulting positions to the OnlyCSharp 1.7 ray tracer, which path-traces the shot and writes it into an animated GIF. No positions are lerped and no frames are hand-drawn.
Everything leans only on the frozen OnlyCSharp 1.7 libraries - PhysicsAndAstronomy.Physics, Mathematics.Fast.Dynamics, ComputerGraphics.RayTracer and ComputerGraphics.ImageCodecs - which depend on nothing outside the .NET base class library. The collision impulses use the standard normal-impulse law, the wave field honours its CFL condition with reflective walls, and the gravity flybys conserve momentum. The physics is auditable line by line; the renders below are just what those numbers look like.