Fig 1.
[1] Moore and Von Neumann neighborhoods at D = 1 and D = 3. In this paper, we use Moore neighborhoods consistently. [2] Three simulation agents: ‘A’ has 16 like-neighbors out of 24, ‘B’ has 6 like-neighbors out of 21, and ‘C’ has no neighbors. With an intolerance threshold of 0.35, ‘B’ is forced to move, while ‘A’ and ‘C’ remain at their current locations. [3] In a more populated world, ‘B’ is deciding where to move. Of the locations ‘B’ considers, ‘1’ and ‘2’ will not satisfy its intolerance threshold, but ‘3’ will.
Fig 2.
[1] A set of individuals and a blue venue. Each individual has its own surroundings and the venue has a catchment area that is determined by the maximum travel distance. [2] If this venue is completely obligatory and exclusive, every blue individual within the catchment will visit during each time-step. Blue individuals beyond the catchment area (such as ‘C’) are unable to visit. Evaluating their positions, ‘A’ has 4 like-neighbors of 11, but also 18 like-neighbors added from the venue, yielding a score of 22 of 29. ‘B’ has 3 like of 8, but also 18 from the venue, resulting in a score of 21 of 26. ‘C’ has 2 like-neighbors of 8, with no contribution from the venue because it is unable to visit. [3] If ‘C’ moves this turn, it will consider destinations within the catchment distance of the venue and also beyond in a random order. In evaluating the former, such as location ‘1’, it will consider the influence of individuals from the venue, making it a very good destination, while ‘2’ which is just beyond the venue catchment will not benefit from the additional count, and will hence not be a likely choice.
Fig 3.
Flowchart of a single timestep in the simulation model.
Chart elements shaded in grey are typical of Shelling implementations while our own additions have a white background.
Fig 4.
Illustration of concordance and predominance.
We can measure the concordance of agents A and B by counting what proportion of their immediate neighbors are members of the same group. In the case of A, we have 6 of the same group and 2 of the opposite group, making a total of 8. The concordance of A is hence 6/8 or 0.75. In the case of B, we have three of the same group, and 1 of the opposite group, for a total of 4. The concordance of B is hence 3/4 or, in other words, also 0.75. When it comes to measuring predominance, some area of the simulation world must be identified where the count will take place. In this case, an outlined area is indicated in bold. Predominance is determined by first counting the number of agents in the area of each group. Here, we have 6 red and 13 blue. The predominance in this case is therefore, (13–6)/19, or 0.37.
Fig 5.
In reporting our study results, we follow a consistent layout and utilize a repeated set of analytics, illustrated as an empty framework here.
In the top left, specific simulation parameters that vary in the study are listed. These variables become the X and Y axis of subsequent charts. Complete simulation settings are available in the S1 Appendix. Below the parameter settings, we illustrate the locations of venues for this study. To the right of these “input” settings, we illustrate parameter space results for the study. These charts show how values of Concordance, Predominance, and volatility (in terms of Standard Deviation) change with different values of the input parameters, where grey-scale values indicate average values across multiple runs with randomized initial distributions of agents. Dashed shapes within the parameter space indicate that a subsequent chart will focus on a smaller region of the full parameter range, while red letters in square brackets connect with specific images of simulation results illustrated in a companion figure (in this case, in Fig 6 below).
Fig 6.
Here we illustrate actual resulting configurations of the simulation world for different input parameter values.
These result images are keyed to the parameter space illustrations (introduced in Fig 5 above) through the letter system in square brackets to the bottom left of each. Beside this number, x and y values indicate the exact values for the variable input parameters that yielded the outcome. Finally, mechanisms that are catalogued and described as part of our results are also indicated here for the sake of quick reference.
Fig 7.
Study 1 simulation settings and resulting parameter space.
For additional simulation settings, see the S1 Appendix. Letters in square brackets within the parameter space refer to specific simulation runs that are illustrated in Fig 8.
Fig 8.
Results sampled from Study 1, comparing different values for individuals’ intolerance (x) and the maximum travel distance to venues (y).
In the first view, [A], we see classic Schelling-style segregation, [B,C] the influence of venues as travel distance increases, [D] an area of low intolerance, [F,G] “locked-in” situations that in [E,H,I] are “unlocked” by the influence of venues, which “bootstrap” new neighborhoods. Each of the letters in square backets can be used to locate these specific results in the larger parameter space by referring back to the red letters in Fig 7.
Table 1.
Generative processes discovered during the simulation case studies.
Fig 9.
Study 2.1 simulation settings and resulting parameter space.
For additional simulation settings, see S1 Appendix. Letters in square brackets within the parameter space refer to specific simulation runs that are illustrated in Fig 10.
Fig 10.
Some results for the radial distribution.
[A] shows the influence of a radial arrangement of venues on Schelling-style integration, while [B,C] show bridging and take-over situations in the core. Each of the letters in square backets can be used to locate these specific results in the larger parameter space by referring back to the red letters in Fig 9.
Fig 11.
Study 2.2 simulation settings and resulting parameter space.
For additional simulation settings, see S1 Appendix. Letters in square brackets within the parameter space refer to specific simulation runs that are illustrated in Fig 12.
Fig 12.
Some results from the core-periphery model.
While study 1 yielded core-periphery patterns, here we test reinforcing this tendency with venues. We note cases such as [A,B] where a fully integrated core does not yet emerge, and [C] where it does. Between [D,E, and F] we note a shift in terms of the relative influence of core and periphery on the overall Concordance. Each of the letters in square backets can be used to locate these specific results in the larger parameter space by referring back to the red letters in Fig 11.
Fig 13.
Study 3 simulation settings and resulting parameter space.
For additional simulation settings, see S1 Appendix. Letters in square brackets within the parameter space refer to specific simulation runs that are illustrated in Fig 14.
Fig 14.
Some results of the second study, comparing different values for individuals’ intolerance and the exclusivity of venues associated with Group 2 (blue).
The focus of this study is the sharing or co-opting of less exclusive venues by another group and the influence this has on the distribution of individuals. In the views above, we see this playing out in different ways: in [A], a sharing of low exclusivity venues amongst individuals of threshold-levels of intolerance, [B,C,D] the other side of the threshold, where the tipping of the venues leads to segregated outcomes, [E] an asymmetrically locked-in condition, and [F,G,H] various levels of neighborhood evacuation and co-opting by another group. Each of the letters in square backets can be used to locate these specific results in the larger parameter space by referring back to the red letters in Fig 13.