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NetLogo Models Library:
This model is from Chapter Three of the book "Introduction to Agent-Based Modeling: Modeling Natural, Social and Engineered Complex Systems with NetLogo", by Uri Wilensky & William Rand.
This model is in the IABM Textbook folder of the NetLogo Models Library. The model, as well as any updates to the model, can also be found on the textbook website: http://www.intro-to-abm.com/.
Like the main DLA model, this model demonstrates diffusion-limited aggregation, in which particles moving (diffusing) in random trajectories stick together (aggregate) to form beautiful treelike branching fractal structures. There are many patterns found in nature that resemble the patterns produced by this model: crystals, coral, fungi, lightning, and so on.
This model is called DLA Simple because it is it is a simplified version of the main DLA model from the NetLogo models library. In the main model, new particles are created as existing particles aggregate. In this model, particles are only created at the beginning. The main model is more computationally efficient, but the rules that drive the phenomenon are more digestible in this model.
Press SETUP to make the initial seed and NUM-PARTICLES particles, then press GO to run the model. The WIGGLE-ANGLE slider controls how wiggly the paths the particles follow are. If WIGGLE-ANGLE is 0, they move in straight lines. If WIGGLE-ANGLE is 360, they move in a totally random direction at each time step.
Note that the resulting structure has a branching structure, like a tree. Why does this happen?
What other phenomena in the world do the shapes remind you of? Is this aggregation process a plausible model of how those phenomena occur?
Try different settings for how much the turtles turn as they do their random walk (the WIGGLE-ANGLE slider). What is the effect on the appearance of the resulting aggregate? Why?
Does it make any difference whether there are more or fewer particles? Why or why not?
What happens if you start with more than one "seed" patch? What happens if the seed is a line instead of a point?
Can you find a way to modify the code so the resulting pattern spirals out instead of radiating straight out?
The rule used in this model is that a particle "sticks" if any of the eight patches surrounding it are green. What do the resulting structures look like if you use a different rule (for example, only testing the single patch ahead, or using
neighbors4 instead of
Can you compute the fractal dimension of the aggregate?
If instead of using green, you gradually vary the color of deposited particles over time, you can see more vividly the accretion of "layers" over time. (The effect is also visually pleasing.)
The model will run faster if the turtles are invisible, so you may want to add a switch that hides them (using the HT command).
Note the use of the
The various models in the "Fractals" subsection of the "Mathematics" section of the Models Library demonstrate some other ways of "growing" fractal structures.
The "Percolation" model in the "Earth Science" section produces patterns resembling the patterns in this model.
This model is a simplified version of:
The concept of diffusion limited aggregation was invented by T.A. Witten and L.M. Sander in 1981. Witten, T. & Sanders, L. (1981). Diffusion-limited aggregation, a kinetic critical phenomena. Phys. Rev. Lett. 47(19), 1400–1403 (1981).
Tamas Viczek's book "Fractal Growth Phenomena" contains a discussion, as do many other books about fractals.
This model is part of the textbook, “Introduction to Agent-Based Modeling: Modeling Natural, Social and Engineered Complex Systems with NetLogo.”
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For the model itself:
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Copyright 2006 Uri Wilensky.
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