DLA Simple

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WHAT IS IT?

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. 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.

HOW TO USE IT

Press SETUP to make the initial seed, then press GO to run the model.

THINGS TO NOTICE

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?

THINGS TO TRY

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?

EXTENDING THE MODEL

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 neighbors)?

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).

NETLOGO FEATURES

Note the use of the neighbors primitive.

RELATED MODELS

The DLA model is a more complicated (but more computationally efficient) model than this one.

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.

CREDITS AND REFERENCES

The concept of diffusion limited aggregation was invented by T.A. Witten and L.M. Sander in 1981. Tamas Viczek's book "Fractal Growth Phenomena" contains a discussion, as do many other books about fractals.

HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

• Wilensky, U. (2006). NetLogo DLA Simple model. http://ccl.northwestern.edu/netlogo/models/DLASimple. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
• Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

Copyright 2006 Uri Wilensky.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

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