A3 | geobbo

ASSIGNMENT 3: PATTERN-ORIENTED MODELING WITH AGENTS

Can you explain what this code accomplishes?

The code determine the movement of the turtles over world - their direction (angle to alter their direction: rt, lt random Number + lenght of movement: forward 0.25).

If Directed-Walk? is ON, the turtle follow 1st command [rt random 90 l random 90], if it is OFF, the turtle folow the second command [rt random 360].

If Directed-Walk? is turn ON it simply means that turtles can change its direction to 90 degrees left or 90 degrees right, if it is OFF it can change the direction of 360 degree.

In both case it moves forward 0.25 patch. If Directed-Walk? is ON, the turtles can easier get out from the centre and the NND is increasing more rapidly as it is in the case od Directed-Walk? turn OFF.

Objective: To determine a process that produces a particular spatial pattern.

Describe in 4-5 sentences the utility of using a pattern oriented modeling approach for understanding the observed patterns of both species.

Different processes could produce similar patterns, if we are focused only in one type of pattern (i.e. temporal, spatial, statistical…) . Hovever, if we observe the process through different viewing angle at the same time, we describe the same process by combination of patterns. It is exactly the combination of these patterns which is crucial to identify underlying process and could be characteristic for the unique species.
creation and modification of individual traits leads to reation of different pattern. If we know already specific pattern for the concrete species, we choose the most alike pattern and through its alikeness we can understand the underlying process (producing the pattern)

For each movement model, describe how agent interactions lead to emergent patterns in both space and time.

Random walk (Directed-Walk? OFF)

For a long time the agents stay close one to another, due to forward movement (.25) and due to possibly turning angle (360°) resulting in gradually increase of NND (green circle) and not in steep one. They are not programment actively looking neither for the food neither for the comrads. They don't actively create the clustered spatial pattern. They are just randomly clustered and each individual can change its 'membership' to specific cluster. Over certain ime they reach "stable" NND value because of possible displacement over the 'word', with mean NND ~ 4 patches, max NND ~ 11 patches, Figure B).

Random walk (Directed-Walk? ON)

Turtles starts to be better separated in space because or less possibility to randomly set ther direction value (only 90 + 90 = 180 instead of 360, steep NND increase in the plot). However they still don't look for the ressources, netheir they don't look forward to be close to their neighbours. Clusters are created non-intentionally with mean NND ~ 4 patches, max ~ 9 patches.

Foraging OFF

In foranging method turtles don't really look for ressources. Once their energy = 0, ther are directly displaced to the closest resource patch to gain the energy. Equally the NND value decrease markantly. The first decrease (NND = green cicrle) is caused by the synchoronized timing of decreased energy for all turtles, as they are loosing energy at every movement.

In the moment of decrease we couldn't really say if the turtles are colonising several patches or only one because we observe only NND, not number of the turtles in patch vicinity. Colonisation of the patch depends on initial random distribution of patches (close or far away from the [0,0] centre). If only 1 patch is close to the 0,0 then only this will be firstly colonised. The next patches will be colonied subsequently, after taking energy from the closest patch.

Foraging ON

Turtles move more 'directed' away from the center [0,0] in randomly selected 180 (90 + 90) degrees. Mean NND increase to 4-5 patchess. After cca 200 ticks, majority of the turtles is out of energy, thus they are displaced to nearest patch - the NND is rapidly decreasing and close to 0. As the turtles - once full of energy - could move far away from the source, the NND increasing, however distupted by iteration of the turtles displacement to the patches = close NND (green cercles). This behavior produces cyclic increase and decrease in mean NND plot.

A) slowly increasing NND over time

B) stable NND over certain time - indication the possibly distribution over available space

A) steeply increasing NND over time

B) stable NND sooner than when Directed-Walk? OFF- indication the possibly distribution over available space

Flocking

In flocking behaviour, the agents are activelly looking for their neighbourhood to create "flock"and are modifying their behavior to stay in their vicinity. Spatially, pattern start with all possible direction so the agents are not close to each other (rapid increase in mean NND values). With trespassig of the 'world boundary' thay have a chance to meet each other and adapt their behaviour to be merged with their comrades following rules: separate, aligne, cohere.

In this reason, during the first time steps NND is rising but finally the agents keep very relatively close NND distances (~ 1.3 patches). Their are activelly changing their reactions in flight directions - following vicinity and directions of their comrades.

Which movement model best describes the patterns observed for species A? Why?

The Foranging behavior (Directed-Walk? turn ON) the best decribes temporal and spatial behavior of species A. The temporal behavior is characterised by cyclic decrease and increase of NND, which can be explain by turtles 'displacing' to patches if their energy is 0.

Foraging Directed-Walk? ON

Which movement model best describes the patterns observed for species B? Why?

The emergent patterns are spatially more or less clustered. Over the time, the NND (near-neighbor-distance) is increasing until the moment of the ideal (mean NND) spatial distribution and the become trend is parallel to axe X.

The most responding pattern to species B is Random walk (Directed-Walk ON). Range of NND is increasing over time (small waves to larger ones), the spatial pattern is forment by small unstable clusters of turtles. Clusters are not stable by their individuals - individuals are migrating, clusters are producing more randomly. (e.i. in Flocking, clusters of turtles are creates mainly by same turtles in one flock over most of the time.) The curve can be simplyfied into curve of species B.

Random Walk, directed-Walk? ON

How did a pattern oriented modeling approach allow you to determine the answers to (iii) and (iv)?

Pattern objected-modeling appoache allowed me to observe and monitor both:

spatial behavior: turtles movement (direction, speed), clustering/aggregation and
temporal pattern of selected spatial characteristic - in this case nearest-neighbour distance (NND).

A small change in individual turtle movement (directed-Walk? ON or OFF so the possibility to change direction, energy counting and influence on turtles displacement if energy = 0) produced different spatio-temporal patterns.

If we already know the spatio-temporal pattern of selected species, by simulation approach - trial and error method - we can modify lows of turtles behavior until the desired behavior will be produced. In this way we can discover the lows of real species behavior.

NOTES

maximal NND of randomly distributed turtles (get by ask turtles [ setxy random-xcor random-ycor ]) is ~ 9 patches.
There is another possible measures to characterize "turtle (dis)aggregation" : maximum and minimum NND distances. Especially maximum NND is interesting because it informs us about the presence/absence of individuals not being part of the cluster, mainly in flocking behaviour (Figures A and B). Equally, it can be interesetd to calculate at each time step the % of agents in certain distance from the patch (in foraging behavior) to decribe their distribution about the space.

A) huge max NND values - indicate the presence st leat one agent not being the part of the flock

B) after certain time, all agents are creating one fock with small NND. The agents are not necessarily to stay in the flock over time

possibility to temporally locate the existing spatial pattern (Fig. 1) or to scale the resulting plot to better understand the increasing distances between the turtles. This approach can be useful mostly in RandomWalk when the distances are increasing over the time until reaching the optimal NND value - parallel to axe X.

Fig. 1 Uncertainity about the 'placement' of the static spatial pattern in temporal pattern.