Courses/CS 461/Winter 2006/Brian Smith/Week 2
From CSWiki
Contents |
[edit] New Segregation Fields model
This model expands on Schelling's Segregation by giving unhappy people some intelligence in choosing a new location. In the existing model unhappy people move to a random spot--even if the new spot has far more different neighbors than their comfort threshold. Not only will this person move again, but all the new neighbors (that were in a comfortable neighborhood) also move away, perhaps to undesireable locations. This unfortunately means that the model runs much longer than necessary. This behavior also seems unrealistic to me when trying to model segregation.
In the new model each person generates a field that affects its patch and neighboring patches. For red people these patches take on a red color, and green people generate green patches. The field is diffused once to spread the values to neighboring patches, including empty patches. When an unhappy person is moving they pick a random empty patch with a field that matches their color. This provides a much higher chance that their new location will be desirable and they will stay. It also prevents a person from moving into an area with a high number of people of the opposite color.
For example, let's say we create 2000 people who desire 100% of their neighbors to be their color. In the Schelling model the random moves mean that people stay scattered: percent similar stays at 50% and percent unhappy stays at 97%. In the new fields model groups begin to form in the first few steps signified by red or green shades in the background. Unhappy people move to the edges of these groups and the field becomes stronger. Eventually the only people moving are on the black borders between red and green and they eventually settle down in desireable spots. If we increase the count to 2500 people, there isn't enough empty space to create black borders and the people on the edges never stop moving.
I changed one person's shape into a circle so it can be tracked step by step.
Segregation Fields applet and source code
[edit] 1000 people, 50% similarity desired
[edit] 2000 people, 40% similarity desired
[edit] 2000 people, 100% similarity desired
Here the fields and black borders are very pronounced
[edit] Updates
After discussing the model with Russ he gave me a few improvements. "random-one-of" has been replaced by "min-one-of" and "max-one-of" to optimize each unhappy person's choice of a new location. He also suggested diffusing the field more. These changes gave the model a significant speed increase, especially when dealing with large populations.
Optimized Segregation Fields applet
[edit] Improvements
I think this is a more realistic model of segregation. One improvement I might make is to allow each person to decide a random similarity percentage (instead of all people being comfortable with the same percentage of similar neighbors). This change would result in areas of diversity and others of strict segregation, like the real world.
[edit] 1. Segregation Fields Analysis
[edit] Emergence
The overall emergent phenomena of this model is the formation of segregated areas of similar people. The degree of segregation is based on the percentage of similarity desired by the agents. A low desired percentage leaves the board nearly unchanged with a random scattering of agents. A high percentage gives rise to completely separated colors. This is possible even with large populations in the fields model. Any empty space is used to maintain a kind of no-man's land between colors.
[edit] Rules
The percentage of desired similarity is set during setup and is universal for all agents. This agent property specifies the percentage of the agent's neighbors that must be of the same color for the agent to stay at their current location. If there are enough neighbors of the opposite color to lower this percentage below the desired percentage, the agent moves to a new location.
In the fields model the agent chooses a new location that is most likely to meet this desired percentage. Each agent gives off a field value of their color that is diffused with the surrounding patches. When an unhappy agent moves it looks for the empty patch with the highest field of its color. This gives the agent the best chance of being happy at the new location.
[edit] Connection
The rules give rise to various levels of segregation because agents will move away from different neighbors based on their desired similarity. They move to the location with the highest concentration of like-colored agents and away from different-colored agents, the essence of segregation. They continue to move if they are unhappy in the new location, so there is no chance that an agent will stay in an integrated place under their desired similarity. The no-man's land phenomena occurs when agents desire a very high percentage of similarity--those on the borders of groups will continue to move if there is an agent of the opposite color adjacent to their patch. If there is enough empty space on the board it will eventually be left between areas of opposing colors as these agents move away.
[edit] 2. Local Genetic Drift Analysis
[edit] Emergence
The most obvious emergent phenomena is that colors quickly form into contiguous groups, and one color can eventually dominate the board. The dominance of any color may oscillate as time progresses. A phenomenon closely linked to this dominance is the extinction of the other colors once they no longer have a patch on the board.
[edit] Rules
The patches are initialized with a random color. The total number of colors present on the board is set by the user. At each cycle every patch chooses a color from its eight neighbors and changes to that color. This continues until the board is composed of only one color.
[edit] Connection
Each patch randomly chooses a color to adopt, but any slight advantage in numbers can lead to dominance for that particular color. Since extinction of colors is possible the number of competing colors decreases and gives the dominant color a chance to control the board. The rules only allow local colors to be chosen, so contiguous groups are reinforced as patches choose neighbors that are the same color. These groups gradually grow larger as other colors become extinct, eventually allowing one color to dominate the board.
[edit] 3. Fireflies Analysis
[edit] Emergence
The emergent phenomena of this model is the synchronization of flashing among fireflies that begin with random cycles.
[edit] Rules
This model offers a choice among methods that the fireflies can use to synchronize with other. In the phase delay model when a firefly sees a set number of other fireflies flashing within a one patch radius it will reset its clock to the set delay time. In the phase advance mol
[edit] Connection
When a firefly sets its clock to the delay time, it ensures that it will flash with the other flashing fireflies that it observed and become synchronized with them. In the phase advance method the firefly flashes immediately with similar effect. Since these rules apply to a firefly's neighbors it is transferred locally until it comes to dominate the board.
