# Introduction to Complex Systems

Prof. Dirk Brockmann, Winter Term 2021

# Practical Problem 4: Percolation

In this example we 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.
4. The probability P should be adjustable with a slider
• define an "anmalen" 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.