I chose to study the effect of two parameters on the simulation. I've examined the effect of change in the number of times a walker must cross an envelope segment before lubricating a new lattice point. Another "experiment" I did is to examine the effect of food concentration. I've conducted both experiments with the default values (lattice size=100x100, food token=10, divide energy=20, initial number of walkers=1, initial energy=20)
In this experiment I've captured the state of the colony every 300 steps, with different lubrication parameters, I used initial food concentration = 30000 for all experiments. From this experiment we can also learn about the evolution of the colony over time.
These are the results:
(a) Parameter=0: step=300
(b) Parameter=1: step=300, step=600
(c) Parameter=2: step=300, step=600
(d) Parameter=3: step=300, step=600, step=900
(e) Parameter=4: step=300, step=600, step=900, step 1200
...
(f) Parameter=5: step=300, step=600, step=900, step 1200 and step 2100
Fig. 1
We can clearly see that the lubrication parameter affects dramatically the diffusion constant: As can be seen in Fig. 1a, the colony spreads over the entire lattice, whereas in Fig. 1f, the colony is very small.
Another thing we can see that with lower parameter value there more forks.
A low value for the lubrication parameter means that the colony needs less energy to spread, which means that it can consume less food particles to spread. So, with low value the conditions are "good" there is plenty of food and it is easy to spread. In these conditions, as I mentioned in the Introduction we wouldn't see any patterns - the colony will do a normal diffusion. We can see this very nicely in Fig.1a and Fig. 1b.
In the higher values images we can see nicely the growth of the colony over time.
In the second experiment I've changed the initial number of food particles and watched the colony state after 900 steps. I kept the same lubrication parameter ( =3) on all experiments.
These are the results:"
Initial number of food particles: 10000, 20000, 30000, 40000, 50000, 60000
Fig. 2
Again we can see that the concentration of food particles affects dramatically the size of the colony. In this case with a low concentration of food the colony didn't grow. We can also see that with higher concentration the colony growth goes toward a normal diffusion (Gaussian distribution around the center) as we expect in the case of ideal conditions.