Carbon sp² Self-Assembly Simulation

What if you could watch carbon atoms find each other, align their bonds, and spontaneously assemble into the strongest material ever measured — all in your browser? No textbook diagrams, no static images. Just raw physics playing out in real time.

What Is This?

This is an interactive particle simulation of carbon atoms with sp² hybridization — the bonding geometry behind graphene, nanotubes, and fullerenes. Each atom carries three bonding directions separated by 120°, mimicking the planar trigonal symmetry of real sp²-hybridized carbon. Drop hundreds of atoms into a box, tune the physics, and watch what emerges. Depending on the parameters, you might get a pristine hexagonal lattice, a pulsating collective oscillation, or tiny crystalline islands floating in a sea of disordered atoms.

Nothing is scripted. Every structure you see is an emergent result of two competing forces and rotational torque working together.

How It Works

Repulsion prevents atoms from overlapping. It's isotropic — it pushes equally in all directions, and gets stronger the closer two atoms get. Think of it as the electron cloud saying "back off."

Attraction pulls atoms toward an equilibrium bond distance, but here's the key: it's anisotropic. Each atom has three preferred bonding directions at 120° intervals, and the attractive force is strongest when a neighbor lines up with one of those axes. Both atoms need to agree — the force depends on the angular alignment of both particles, which is what drives the hexagonal geometry.

Torque rotates each atom to align its nearest bonding axis toward nearby neighbors. This is what breaks the initial randomness and allows large-scale crystalline order to develop from a chaotic starting state.

Friction dissipates kinetic energy so the system can settle into equilibrium rather than bouncing around forever.

The Presets

Graphene Lattice — The showcase. Strong repulsion, tight angular sharpness, and balanced attraction produce a honeycomb lattice that self-assembles from random initial conditions. This is the structure that makes graphene the wonder material it is.

Breathing Mode — Turn this on and wait. The atoms slowly compress under strong attraction, forming a dense cluster. Then, without warning, a shockwave nucleates at a single point and rips through the lattice, scattering atoms outward. Friction slows them down, attraction pulls them back in, and the cycle repeats — roughly every five seconds. The kinetic energy plot lights up with sharp periodic spikes. It's mesmerizing.

Liquid Phase — Low angular sharpness means the bonds don't care much about direction. Atoms clump together but can't form crystalline order. The result is a fluid-like state where clusters constantly form, merge, and break apart.

Hot Gas — Minimal friction and weak attraction. Atoms ricochet off each other and the walls, rarely forming lasting bonds. Pure kinetic chaos.

Nano Clusters — A tight bond distance with strong directional selectivity produces small crystalline islands — essentially graphene quantum dots — that self-assemble but remain separated. They drift, rotate, and occasionally exchange atoms, but never merge into a continuous sheet.

Play With It

The real fun is in tweaking. Slide the parameters while the simulation runs and watch the system respond in real time. Push attraction up and watch atoms collapse inward. Crank angular sharpness and see disordered blobs snap into hexagons. Drop friction to zero and let chaos reign.

There are more phases hiding in this parameter space than the five presets — go find them.

Enjoy playing with your carbons!