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This one is easy you simply set the number of agents or particles and then setup the central cell as on which motivates the development of the city. Agents swirl randomly in the space around this central site and eventually one touches and then sticks. Another particle is launched and the random movement continues until another one sticks to the growing cluster.
You can wiggle the particle by choosing the angle so experiment with this, and you can use the whole world or just grow the city in its immediate vicinity there are lots of options that you can explore and which have an impact on the resultant form.
Our book Fractal Cities contains a complete explanation of how this diffusion limited aggregation might be used as an analogue of the growth of cities.