Diffusion-Limited Aggregation

Watch Fractal Growth Through Brownian Motion

Growth Mode
Multi-Seed
Analysis

About Diffusion-Limited Aggregation

DLA is a process where particles undergoing random Brownian motion stick together to form intricate fractal structures. This simulation demonstrates the classic algorithm:

  • Random Walk: Particles move randomly until they touch the aggregate
  • Sticking: Upon contact, particles adhere with a probability you can control
  • Fractal Growth: Creates branching patterns similar to lightning, crystals, and coral
  • Natural Examples: Snowflakes, lightning bolts, electrodeposition, crystal growth, bacterial colonies
Arrival Time
Distance from Center
Branch
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Total Particles
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Particles/Second
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Max Radius (px)
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Fractal Dimension

Competing Growth Centers

Multiple seed points create competing aggregates that grow and interact. Watch how they form boundaries and create complex interference patterns. This models phenomena like crystal grain boundaries and competing bacterial colonies.

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Total Particles
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Largest Cluster
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Active Clusters

Fractal Dimension Analysis

DLA structures exhibit fractal properties with a characteristic dimension around 1.71 in 2D. The fractal dimension describes how the mass scales with radius: M ∝ RD, where D is the fractal dimension. Compare this to regular shapes (D=2 for filled circles) to see the sparse, branching nature.

  • Box Counting: Classic method for measuring fractal dimension
  • Mass-Radius Scaling: How particle count grows with distance
  • Expected D ≈ 1.71: Theoretical value for 2D DLA

DLA Structure

Mass-Radius Plot (log-log)

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Measured Dimension
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Particles Analyzed
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Max Radius
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R² (fit quality)