Practical Problem 9: Rock Paper Scissors

In this problem we will implement a simulation in which agents of three different types: A, B, and C move around randomly and interact in the rock-paper-scissor fashion we discussed in class:

[ A+B\xrightarrow{\alpha}2B\quad B+C\xrightarrow{\alpha}2C\qquad C+A\xrightarrow{\alpha}2A ]

So when for example a turtle of type A encounters a turtle of type B the latter will convert to an A turtle.

Todo:

1. Start by writing the usual template for the go and the setup function, not forgetting the commands ca and reset-ticks in the setup function and the tick command in the go function.
2. add buttons for the go and setup function in the interface. Also add four sliders for controlling 4 parameters
   • the speed of the agents
   • the wiggle (randomness) of the movements
   • the interaction radius
   • the number \(N\) of agents of each type. So for instance when \(N=100\) the system should be initialized with 100 agents of each type.
3. In the beginning of your code use the code snippet below to define a turtle specific variable called typ:

turtles-own [typ]

3. Write a setup function that creates \(N\) turtles of each type using statements like create-turtles N [set typ "A"] for example. The turtles shoud be placed at randon positions ask turtles [setxy random-xcor random-ycor]
4. Write a function that paints turtles according to their type. This function should be called at the end of the setup routine and the go routine.

to paint
    ...
end

5. Write a go function that does the interaction. The go function should loop over all the turtles. For each interaction the current turtle should pick a random target in an interaction radius \(R\). Remember you can check this out by

let target one-of other turtles in-radius R
if target != nobody [
    ...
]

5. then you should compare the type of the current turtle with the type of the target and implementing the rock-paper-scissors rules update their state
6. If you want, you can setup a switch on the interface that sets a boolean variable. You can call this variable trace and add the following code to your turtle update loop

ifelse trace = True [pen-down][pen-up]

7. You can also add a button that deletes all the traces. This is something you can find in the user manual of netlogo.

Simulation 2

Write a patch based simulation in which patches are either A, B or C. As in the turtle simulation initialize the system fairly.

At each type step a pache react with a randomly chose neighbor (ask one-of neighbors [...]) and changes its state according to the above reactions.