A flock finds order: polarization from chaos

Completed

Seed: 42
Steps: 600 / 600
Created: 26 July 2026 at 08:07
Finished: 26 July 2026 at 08:07

Hypothesis

Three purely local, instantaneous rules, with no central coordination and no learning, are enough for ordered collective motion to emerge from random initial velocities

Vital signs

Order parameter0.67

View data

Order parameter by step
Step	Order parameter
10	0.03
20	0.07
30	0.09
40	0.10
50	0.07
60	0.08
70	0.11
80	0.06
90	0.10
100	0.08
110	0.03
120	0.04
130	0.02
140	0.02
150	0.03
160	0.02
170	0.05
180	0.03
190	0.08
200	0.05
210	0.03
220	0.06
230	0.18
240	0.17
250	0.12
260	0.08
270	0.01
280	0.08
290	0.12
300	0.23
310	0.23
320	0.27
330	0.26
340	0.36
350	0.22
360	0.41
370	0.29
380	0.33
390	0.56
400	0.50
410	0.53
420	0.70
430	0.61
440	0.61
450	0.72
460	0.62
470	0.68
480	0.71
490	0.60
500	0.77
510	0.63
520	0.64
530	0.77
540	0.57
550	0.67
560	0.70
570	0.72
580	0.67
590	0.73
600	0.67

Number of clusters6.00

View data

Number of clusters by step
Step	Number of clusters
10	1.00
20	8.00
30	6.00
40	8.00
50	9.00
60	10.0
70	9.00
80	6.00
90	5.00
100	7.00
110	7.00
120	7.00
130	6.00
140	6.00
150	5.00
160	5.00
170	6.00
180	7.00
190	7.00
200	6.00
210	7.00
220	8.00
230	7.00
240	8.00
250	7.00
260	7.00
270	7.00
280	7.00
290	5.00
300	8.00
310	9.00
320	9.00
330	7.00
340	7.00
350	6.00
360	6.00
370	6.00
380	6.00
390	7.00
400	6.00
410	7.00
420	7.00
430	8.00
440	7.00
450	7.00
460	7.00
470	7.00
480	8.00
490	8.00
500	8.00
510	6.00
520	6.00
530	6.00
540	6.00
550	5.00
560	6.00
570	6.00
580	7.00
590	7.00
600	6.00

Mean speed1.60 u/step

View data

Mean speed by step
Step	Mean speed u/step
10	1.59
20	1.62
30	1.42
40	1.44
50	1.33
60	1.42
70	1.38
80	1.32
90	1.38
100	1.31
110	1.25
120	1.27
130	1.32
140	1.19
150	1.15
160	1.10
170	1.07
180	1.05
190	1.03
200	1.05
210	1.04
220	1.05
230	1.08
240	1.15
250	1.11
260	1.22
270	1.21
280	1.20
290	1.29
300	1.42
310	1.39
320	1.26
330	1.29
340	1.30
350	1.27
360	1.24
370	1.23
380	1.27
390	1.22
400	1.24
410	1.22
420	1.18
430	1.13
440	1.28
450	1.24
460	1.18
470	1.27
480	1.18
490	1.21
500	1.19
510	1.21
520	1.21
530	1.22
540	1.21
550	1.68
560	1.07
570	1.08
580	1.58
590	1.68
600	1.60

Video captures

Configuration

Parameter	Value
params	{"n":300,"world_size":150,"perception_radius":15,"sep_weight":1.5,"align_weight":1,"coh_weight":1,"max_speed":3,"min_speed":1,"max_force":0.3,"device":"cuda","render_size":512,"traj_stride":2}

Journal notes

26 July 2026A flock finds order: polarization from chaos