Introduction to the Modeling and Analysis of Complex Systems

19.3. AGENT-ENVIRONMENT INTERACTION 443The other way is the chemotaxis, which can be implemented in several different ways. Forexample, we can have each agent look at a cell randomly chosen from its neighborhood,and move there with a probability determined by the difference in cAMP concentration(∆c) between the neighbor cell and the cell where the agent is currently located. A sigmoidfunctionP (∆c) = e∆c/c 01 + e ∆c/c 0(19.1)would be suitable for this purpose, where c 0 is a parameter that determines how sensitivethis probability is to ∆c. P (∆c) approaches 1 with ∆c → ∞, or 0 with ∆c → −∞. Thispart can be implemented in the update function as follows:Code 19.12:# simulating chemotaxis of agentsfor ag in agents:newx, newy = (ag.x + randint(-1, 2)) % w, (ag.y + randint(-1, 2)) % wdiff = (env[newx, newy] - env[ag.x, ag.y]) / 0.1if random() < exp(diff) / (1 + exp(diff)):ag.x, ag.y = newx, newyHere diff corresponds to ∆c, and we used c 0 = 0.1.5. Describe the rules for how agents behave on their own. All the actions taken bythe agents in this model are interactions with the environment, so we can skip this designtask.6. Describe the rules for how agents interact with each other. In this model, agentsdon’t interact with each other directly; all interactions among them are indirect, mediatedby environmental variables (cAMP concentration in this case), so there is no need toimplement anything for the agents’ direct interaction with each other. Indirect agent-agentinteraction through informational signals written in the environment is called stigmergy,which is an essential coordination mechanism used by many social organisms [88].By putting everything together, and adding the observe function for visualization, theentire simulator code looks like this:Code 19.13: keller-segel-abm.pyimport matplotlibmatplotlib.use(’TkAgg’)from pylab import *