Both models grow a cluster one particle at a time on a lattice, but the rule for where the next particle attaches produces wildly different shapes. The Eden model (Murray Eden, 1961) picks the next site uniformly at random from every empty cell touching the cluster — every part of the boundary grows equally fast, so the result stays compact and roughly circular. Diffusion-limited aggregation (Witten & Sander, 1981) instead launches a particle far away and lets it random-walk until it bumps into the cluster and sticks. Tips and outer branches intercept wandering particles before they can reach inner gaps, so growth runs away at the tips — producing sparse, branching, tree-like fractals.
log(N) / log(R), where N is the particle count and R is the cluster's radius — Eden clusters trend toward D≈2 (space-filling), DLA clusters trend toward D≈1.7 in this 2D lattice.The branching patterns DLA produces show up all over nature at wildly different scales — mineral dendrites in rock, electrical discharge (Lichtenberg) figures, coral growth, and even the shape of some bacterial colonies all follow the same diffusion-limited aggregation rule.
A voxel cluster grows one particle at a time on a lattice — switch between the Eden model's compact, blob-like growth and diffusion-limited aggregation's sparse, branching growth to see how a single rule for "where does the next particle attach?" produces two completely different shapes.
Eden growth fills every frontier cell with equal probability, staying compact with a fractal dimension near 2. DLA growth lets particles random-walk in from a distance, so branch tips shadow inner gaps and growth runs away at the tips, producing a sparser fractal with dimension near 1.7.
Pick a growth model and lattice connectivity, then watch the cluster grow live. Tune growth speed to speed up or slow the process, and adjust DLA stickiness to see denser or lacier branches. Drag to orbit, scroll to zoom, and reset any time.
Witten and Sander's 1981 DLA paper explains an astonishing range of natural branching patterns — from mineral dendrites and electrical discharge figures to coral skeletons and some bacterial colonies — all from one simple random-walk sticking rule.