| Much of the early simulation of DLA involved clusters of modest size - several thousands to tens of thousands of particles. |
| Much larger simulations, in the million particle range, reveal departures from the previous simple picture. |
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| Mandelbrot, Vespignani and Kaufman studied the properties of 50 off-lattice clusters of a million particles and 20 off-lattice clusters of ten million particles. |
| The method of analysis was transverse cross-cuts, intersections of the cluster with the circles centered at the seed. |
| The largest circle was 3/4 the radius of the cluster, so only the fully-grown parts of the cluster were studied. |
| If large DLA clusters were statistically self-similar with dimension 1.71, then the transverse cross-cuts should have dimension 1.71 - 1. |
| Instead, a dimension of 0.65 was observed. |
| This suggests a lacunarity effect: as the cluster grows, it becomes increasingly more compact. |
| Additional evidence is provided by measuring the largest gaps. |
| Small clusters evolve toward a five-branch symmetry, so on average we would expect the gap to be about 72°. |
| As the cluster grows, the largest gaps become smaller (the lacunarity decreases) and the cluster develops more arms. |
| The situation is complex, and the work continues. |
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