Fig 1.
Vectors A and B represent agents in attribute space.
R is the vector distance between agents and represents their difference in attributes. The force FAonB of agent A on B is shown in blue. The agents are allowed to communicate since R <AIB. a) The force is attractive since ω < 90°; b) The force is repulsive since ω > 90°.
Fig 2.
The force FAonB in blue changes vector B to B + ΔB in red.
a) attractive force which decreases the angle between A and B; b) repulsive force increases the angle.
Fig 3.
Distribution of Agents at the end of 1000 simulations for AIB = 100, standard conditions: a) Scatter plot of final location. The size of each point correlates with the agent mass; b) Angular distribution in sectors of 30 degrees. 1 means random distribution. The mean for all 12 sectors is 1.00 (random) and the SD 0.06.
Fig 4.
Distribution of agents at the end of 1000 simulations for AIB = 100, standard conditions.
a) Distance from the origin. The mean distance is 52.6, about half of AIB = 100, and the SD 8.2; and b) MDCN = mean distance to closest neighbor. Median MDCN = 98.
Fig 5.
Overlay of multiple simulations to show the effect of variation in the coalescence radius CR, AIB = 120, standard conditions, seed = 61.
A dark grey bullseye indicates the origin (0,0) in the center of the figure and the trail of a small red spot indicates the location of Center of Attributes during the simulation. a) Simulations with CR = 0.1(blue), 0.2(red/default), and 0.3(green). The red covers the blue and green tracks indicating they are almost identical; b)Simulations with CR = 0.2(red/default), 0.7(blue), and 1.5(green). Some differences are visible.
Fig 6.
Simulations for the same FVM force vector law but with three values of the force exponent, with AIB = 100, seed 91.
(a) 1/r0.5. ET = 503, DT ≤ 0.5. (b) 1/r2. ET = 23, 360, DT ≤ 100. (c) 1/r5. ET = 1.3 × !07, DT ≤ 1.28 × 107. (d) Overlay of tracks from all three simulations with red r0.5, blue r2, green r5. The colors of the tracks in a, b and c correspond to the color assigned to each initial agent.
Fig 7.
Overlay of simulations in red, blue, green, and brown, with four different values of g, all have AIB = 100, seed = 71 and 2580 iterations.
The final red tracks cover the blue, green and brown tracks perfectly: 1) red g = 2.0 × 10−5, ET = 57346; 2) blue g = 7.0 × 10−5 (default), ET = 30653; 3) green g = 3.0 × 10−4, ET = 14806; 4) brown g = 1.0, ET = 256.46.
Fig 8.
Simulation at 10% ET of completion.
Groups = triangles, individual agents = circles. Standard initial conditions. Seed = 61. a) AIB = 30, ET = 680, 27 individuals(circles), 26 groups(triangles), MDCN = 12, repulsive force<0.5%, DT<5. b) AIB = 180, ET = 5490, 10 groups, MDCN = 21, repulsive force< 20%, DT< 17. For animation for 30 AIB: https://youtu.be/WzblcRCjiK8.
Fig 9.
Simulation at 50% ET of completion.
a) AIB = 30, ET = 3410, 1 individual, 19 groups, MDCN = 21, repulsive force<0.8%, DT<15. b) AIB = 180, ET = 27041, 3 groups, MDCN = 115, repulsive force≤100%, DT ≤ 110.
Fig 10.
Simulation at 75% of completion.
a) AIB = 30, ET = 5116, 12 groups, 1 individual, MDCN = 28, repulsive force< 0.8%, DT< 20. b) AIB = 180, ET = 40,502, 3 groups, MDCN = 154, repulsive force≤ 100%, DT ≤ 110. For animation of this simulation with AIB = 180 go to https://youtu.be/BArqDp8-JAQ.
Fig 11.
Simulation at 100% of completion.
a) AIB = 30, ET = 6821, 7 groups, 1 individual, MDCN = 38, repulsive force< 0.8%, DT< 20. b) AIB = 180, ET = 54,030, 3 groups, MDCN = 181, repulsive force = 100%, DT ≤ 140.
Fig 12.
Overlay of simulations with AIB = 30(red), 60(blue), 180(green).
a) Seed = 51, Number of final agents = 10(red), 3(blue), 2(green). b) Seed = 71. Number of final agents = 10(red), 3(blue), 3(green).
Fig 13.
Mean number of agents (black) and groups (red) with standard deviations at the end of a simulation as a function of the Attribute Influence Bound (AIB).
Standard Conditions, 100 runs/AIB value: a) AIB from 0 to 100; b) AIB from 50 to 280.
Fig 14.
Ln(Mean number of agents—2.2) versus AIB, black points with standard deviation are data and red is a linear fit.
Standard Conditions. Illustrates the exponential decrease in the number of final agents from 98.6 to 3.2 as AIB increases from 1 to 52.
Fig 15.
Histograms of angle and mass for final states with three agents: a) Angle between adjacent agents. Mean = 120°, SD = 17.5°. b) Mass of final agents. Mean = 2000, SD = 653 3 final agents.
Fig 16.
Mean distances at the end of a simulation with standard deviations.
Orange = Mean Distance between Agents; Blue = Mean Distance to Origin; Red = MDCN Mean Distance to Closest Neighbor. a) AIB from 0 to 100. b) AIB from 0 to 280.
Fig 17.
The ratio MDCN/AIB = Mean Distance to Closest Neighbor/AIB as a function of AIB, standard conditions.
Fig 18.
Overlays of simulations with (in red) and without (in blue) repulsive forces.
Seed = 91, Standard Conditions. a) AIB = 30; b) AIB = 60; c) AIB = 180.
Fig 19.
Effect of the location of the center of the initial distribution (Xmean, Ymean) on the degree of agreement present at the end of the simulation: a) For consensus (100% agreement); b) For agreement of ≥90% of agents at end of simulation.
Fig 20.
Example of random distribution centered at (20,0) leading to consensus.
Seed = 91, AIB = 60, final location of group = (19.6, 4.9): a) Start and b) End of simulation.
Fig 21.
Effect on final state of adding one agent to the initial configuration.
a) AIB = 30, agent of mass 500 added at (0,30). Compare to Fig 11a. b) AIB = 180, agent of mass 100 added at (0,30). Compare to Fig 11b.
Fig 22.
Attribute sheds present in a simulation with AIB = 200, shown with thick solid lines.
Agent trails show that no agents have crossed these dividing lines during the simulation.