Fractal Pattern Crowd Simulation Model - Coursework Example

ANALYSIS OF FRACTAL PATTERN CROWD SIMULATION MODEL 1. Introduction Initially, the term “fractal” or “broken” in plain English is commonly used to describe a fragmented geometric shape that when taken apart and examined closely each part is similar as shown in Fig. 1 and 2. The model developed by Widyarto & Latiff (2008), is taking advantage of this phenomenon and the similarities between fractal pattern generation and crowd behaviour particularly the interaction among crowd members. Since crowd behaviour in crowd simulation models is considered a collective behaviour from each member of the crowd, an interaction of living systems with many similar units, it is assumed that individual human movement will create a similar fractal pattern. The following sections analyses the usefulness of the fractal model proposed by the above authors in controlling human flow, congestion, enhancing efficiency of emergency evacuation procedures, and avoid fatal catastrophe associated with different crowd behaviours. 2. The logic of fractal pattern crowd simulation model Fractal pattern crowd modelling is a crowd microscopic model that generally considers the interacting forces among members (“agents”) of the crowd. Typical crowd microscopic models are usually focused on modelling the interaction within a crowd and ignoring the possibility of fractal patterns that can predict the behaviour and movement of crowd members with similar characteristics. The fractal pattern as shown below demonstrates the relationship between crowd movements and fractal generation. Figure 1 shows the resulting computer generated self-similarly produced by a number of iterations or recursive processes applied to various points (or particles in microscopic models) in the image following a particular rule. Figure 2 shows nature generated fractal patterns suggesting that there are indeed forces shaping the behaviour of elements in our environment. Figure 1 - A sample computer generated fractal In real-life situation, points used in Figure 1 can represent individual members of the crowd with varying behaviours. The fractal pattern generated when a certain rule (a scenario, behavioural characteristics of each agent or members of the crowd) is applied represents the resulting crowd movement. For instance, members of the crowd with tendencies to move away from the scene of an incident will create a pattern of their own while those with tendencies to move closer as observers of the incident will generate their unique pattern. Similarly, those with tendencies to panic and move towards different directions with create a different pattern from the rest of the crowd. Overall, these varying patterns will create a fractal image as shown in Figure 1 where those encircled represent similar crowd movement based on similar agent or crowd member behaviour. 3. The difference between microscopic SWARM and CROWD modelling Although both microscopic SWARM and CROWD generally focus on the movement of large number of agents, SWARM simulation ignores the potential danger or the possible movement of agents induced by a certain threat such as running back when thick smoke is encountered along escape path during a fire or being motionless when an agent detects danger or obstacles in both paths. This is similar to crowd circling the Kaa’bah (page 319 of Fractal, A Microscopic Crowd Model) where crowd flow is slowed or stopped by obstacles resulting to increased physical interaction and tendency toward mass behaviour or following what others do. In contrast, microscopic crowd models consider every agent as an individual member of the crowd capable of individual and collaborative actions where each agent’s movement is influenced by other agents as well as the environment in which they interact. In other words, the model considers the different forces influencing or encouraging crowd behaviour in a particular situation. 4. The Three Type of Forces Force is crowd simulation models is a basic element that has a direct effect on people’s movement, it greatly influences people’s decision particularly in uncertain situations, and more importantly, it determine the outcome of a dangerous crowd scenarios like the degree of injury or number of fatalities. This is because an agent crowd movement is motivated by internal forces driving them to move toward a certain destination with defined velocity. 4.1 – Force 1 – Main Force and Starting Force As a rule, the two other forces will not work without this force which drives the agents to move forward from its initial position toward the target location due to application of “Alpha force” or the desire to move. That is with speed from zero to maximum walking speed which value varies from country to country (see Table 1, page 321). Note that if there is no Alpha force applied the agent is considered motionless or stationary since there is no known destination. Moreover, if the two other forces (“Chi forces”) are absent, the movement induced by this force will follow a straight line. 4.2 – Force 2 – Repulsive force to prevent collision ) This force generally is the agent’s behaviour to avoid collision but it does not necessarily change the direction caused by Force 1. It merely influence decreased or increased the speed of agent in responding to the threat while maintaining its initial direction. By adding radii of repulsive force of multi-agent reactions (i.e. keeping a safe distance or slowing down then following another slower agent) as shown in Figure 3, collision avoidance is ensured. 4.3 - Force 3 – Repulsive force but with change of direction This type of force is with similar mechanism with Force 2 but with agent’s change of direction. The agents here are given sight and distance influence (environmental awareness as an avoidance rule). The agent will move away or change its direction to avoid collision producing a curved path for all agents that are likely to collide. Agents do not have to be too close to move away particularly when there is enough surrounding space. Their individual velocity direction is matched with nearby agents creating a bend or curve in their path. The amount of repulsive force is equal to the distance between them thus the nearest they become or the larger the radii or influence overlap as shown below, the stronger the repulsive force. In multi-agents environment where these two forces repulsive mechanism may not be very effective, an additional force surrounding the agents is valuable like the influence radius that enables them to keep a safe distance. 5. Crowd Behaviour Model with Fractal Pattern To be able to integrated fractal pattern modelling into existing crowd behaviour model, Widyarto & Latiff (2007) selected a fractal pattern with a pair of arms based on the teaching of the Holy Quran that Allah created “pairs all things” (p.324). Fractal patterns is therefore based on pairing, a pattern that grows and iterated. Similar to the initial starting position of an agent with Alpha force and Chi forces mentioned earlier, the pattern starts with its first branch then grow and create up to two branches toward left and right – repulsive or move away directions. The simulated effects of forward forces (Alpha force only) to agent’s paths as shown in Figure 5 result to a linear line indicating no change of direction while curves are visible when Chi forces (repulsive forces enable move away or change of direction) are applied in Figure 6. However, the effects of Chi forces combined – forward, repulse, and collision avoidance, shows much greater variation in agent’s path that are likely produced by overtaking behaviour of agents as shown in Figure 7. The result of these simulation indicate that paths have similar pattern but not self-similar as in a fractal. In other words, although following the rules each agent’s behaviour is not recursive became every time the rule is applied a new path is being taken. There is thus a need to incorporate fractal’s self-similarity dimension into the crowd model to enable fractal formation. These include considering the functionality STEPS or the specific number iterations (with values ranging from 100, to 10,000) which results are shown in Figure 1 earlier. Another is box counting or the self-similarity dimension (incorporation of number of points and number of iterations) that can provide space-filling in fractal curves. However, the manipulation of branch lengths and angles of the fractal pattern proved useful as shown in Figure 8 providing a clear picture of curve emerging behaviour (repulse, move away, collision avoidance) of agents simulated in microscopic model representing complex structure of crowd path. Figure 8 - Fractal pattern developed when branch (left and right respectively) lengths and angles are manipulated The result of equal arms length with a 60 degree angle is a bee-hive like formation (see Fig. 9) while a same arms length and zero angles produced a straight line. By observation and analysis, such pattern may be produced by creating a set of rules to make agents move in a realistic manner. The rules include: 1. Distinguishing which agents are not reaching the maximal velocity. 2. Distinguishing which agents are slowing down to keep a safe distance. 3. Distinguishing which agents are in a congested situation or with reduced velocity 4. Distinguishing which agents are still moving ahead The logic behind these rules is the fact that flow rate is determined by density or the number of people or agents nearby. Low density means low chances of interaction. Similarly, the flow will become increasingly linear if the density is becoming high because there is limited space for the agents to move. In contrast, when the density is too high, interaction starts and agents lower their velocity, repulsing and avoiding collision more frequently resulting to slower flow rate that will eventually dropped to zero when the path is completely jammed. 6. Conclusion Controlled by set of rules, fractal patterns can be used to predict crowd behaviour similar to existing microscopic crowd models. The advantage of fractal pattern modelling is that it can produce more complicated patterns that can be helpful in determining some unexplained behaviour. For instance, why alternative exits are often ignored or why such a well-planned emergency evacuation procedure end up in fatal catastrophe? The fractal pattern crowd modelling in other words can clearly show the reactions and movement of agents behaving in similar manner (self-similar pattern) in specific situation as in Figure 10. Fractal pattern does show possible crowd behaviour clearly and realistically compared to SWARM with no realistic reactions from agents. 7. References Widyarto S. & Latiff A, 2008, Fractal, A Microscopic Model, Fractals, Vol. 16, No. 4 (2008), pp. 317-332 Read More