Practical Problem 4: Percolation

In this example you will implement a simulation for the process of percolation, see for example the Explorable Barista’s Secret

All we need to do is use patches as agents in netlogo.

To do:

• write a netlogo program in which all patches can have one of three states: “empty”, “coffee” and “water”

• make the world 64x64 in size

• the setup function should initialize all the patches in the following way

  1. patches should either be empty (white) or coffee (brown).

  2. With a probability P they should be empty

  3. A small disk of patches in the middle should all be water (blue). You can filter the patches according to their x and y coordinates. Check the manual for the variables that store these values. You can also use the netlogo function distancexy 0 0 that returns the distance to the origin.

  4. The probability P should be adjustable with a slider

• define a “paint” function that colors the patches accordingly

• The go function should carry out the following algorithm

  1. every water patch should turn all the neighboring empty patches into water.

  2. you can have use a construct like this

    ask patches with [state = "water"] [
		ask neighbors with [state = "empty"][
			...
		]
	]

Observations

Using this simulation, try to find the critical concentration of white patches necessary for the water to reach the boundaries of the system.