An illustrated look at fractal graphene structures, their physics and chemistry, and the Monte Carlo simulations used to model them, shown here as static results.
Read the definitions → See the simulationsGraphene's honeycomb lattice repeats at the atomic scale. Fractal graphene structures extend that self-similarity across multiple length scales — through engineered defects, Sierpiński-style cutouts, or hierarchical assembly — producing materials with tunable electronic, mechanical, and thermal properties that a uniform lattice can't reach.
Recursively removed hexagons create scale-invariant electronic band structure.
Controlled vacancies introduce fractal dimension without changing chemistry.
Graphene flakes arranged in fractal patterns across micro- to macro-scale.
Two reference pages ground the rest of this site: precise, ISO-standard definitions for graphite, graphene, and stacking order, and a survey of how graphene is actually made.
Graphite, graphene, turbostratic/twisted stacking, A-B Bernal and rhombohedral (ABC) stacking, and where "fractal graphene" fits outside the standard.
Read definitions →Mechanical and liquid-phase exfoliation, CVD, roll-to-roll CVD, epitaxial growth on SiC, graphene oxide routes, and more.
Read production methods →Single-layer graphene, the 20–50 nm flake it's built from, and the fractal aggregate those flakes form — on a log-scale ruler, with a live-grown DLA illustration.
See the scale ruler →The σ/π bonding that builds the lattice, van der Waals forces between layers, and the dangling bonds at a flake's edge.
Read about bonding →Additional results below are placeholders pending export to /data.
Two graphene aggregates are built with the same number of particles: a fractal aggregate grown via diffusion-limited aggregation (fractal dimension ≈ 1.7 in 2D), and a non-fractal, compact aggregate — the same particle count packed into a dense disk, standing in for restacked or bulk graphene. Simulated ions diffuse in as random walkers and "activate" a site on contact, a simple proxy for ion adsorption or electrolyte access.
The compact aggregate lights up fast at first but saturates early — its own outer layer screens the interior, so most of its mass stays permanently inaccessible. The fractal aggregate starts slower but keeps climbing, because almost none of its mass is buried; nearly every branch is itself a surface. It eventually overtakes the compact case.
This is the geometric mechanism behind the real-world advantages reported for fractal aggregate graphene: for the same mass, far more of it is usable surface — translating into better ion transport, higher effective capacitance, and greater sensor/catalytic activity per gram than bulk or restacked graphene.
Method: 400×400 grid, ~2,000–2,400 sites/structure · 250 random-walker ions · 45,000 diffusion steps, vectorized in NumPy · rendered at 15 fps with Matplotlib/FFmpeg. Simplified 2D lattice-walk model — illustrative of the surface-accessibility mechanism, not a full MD/DFT simulation.
Simulation results will render here from precomputed JSON.
Simulation results will render here from precomputed JSON.
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