A simulation of diffusion-limited aggregation (DLA) processes that give fractal shapes to mineral dendrites, electrodeposition etc.

1. Diffusion - Limited
Aggregation
Abhranil Das
SPRING 2012

2. Mineral Dendrites
Dendron = plant.
Naturally occurring fissures in limestone and other rock are
percolated by manganese and iron solutions. Often mistaken for
fossils.

3. Branched Electrodeposition
Dendritic structures also form when materials freeze or crystallize out of
equilibrium. e.g: high voltage metal electrodeposition.
Picture: Copper aggregate in copper sulphate solution

4. Simulation
The first computer model was given by Tom Witten at the College dé France and Len
Sander at the University of Michigan (~2000 citations), to describe how dust particles
form clumps in the air.

5. Simulation: Point Seed
Brownian Tree

6. Simulation: Point Seed
Snapshot with 944 drifters and 1131 aggregates, each of radius 0.005 units.

7. Why this shape?
• Why do the branches form?
• Why are they retained? Why doesn’t the shape get filled in?

8. Diffusion to Capture

10. Simulation: Line Seed
Snapshot at dynamic equilibrium with about 250 drifters and 1300 aggregates, each
of radius 0.005 units.

11. Formation of Mineral Dendrites
Solutions of metal and oxide ions diffuse through rock
cracks.
When they meet, they produce a soluble compound.
Beyond a concentration, the compound forms a coloured
precipitate.
On meeting a precipitate molecule, a dissolved compound
molecule sticks to it and adds to the precipitate.
Therefore, the mechanism is the same as electrodeposition.

12. Fractal Dimension

13. Sources
• Branches, Philip Ball, Oxford University Press 2009
• Diffusion-limited aggregation, T.A. Witten, L.M. Sander,
Physical Review B 1983
• classes.yale.edu/fractals