Fermat's Library | Collective Motion of Humans in Mosh and Circle Pits at Heavy Metal Concerts annotated/explained version.

## TL;DR In this paper the authors analyzed videos on YouTube of...

Studies like this that explore emergent behaviors in crowds could b...

An ideal gas is a theoretical gas composed of many randomly moving ...

Notice a clear phase transition from a gas like behavior and vortex...

Here’s a summary of all the emergent behavior that appears when sim...

It’s important to note that most of this work was done based on sim...

Collective Motion of Humans in Mosh and Circle Pits at Heavy Metal Concerts

Jesse L. Silverberg,

Matthew Bierbaum, James P. Sethna, and Itai Cohen

Department of Physics and Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

(Received 13 February 2013; published 29 May 2013)

Human collective behavior can vary from calm to panicked depending on social context. Using videos

publicly available online, we study the highly energized collective motion of attendees at heavy metal

concerts. We ﬁnd these extreme social gatherings generate similarly extreme behaviors: a disordered

gaslike state called a mosh pit and an ordered vortexlike state called a circle pit. Both phenomena are

reproduced in ﬂocking simulations demonstrating that human collective behavior is consistent with the

predictions of simpliﬁed models.

DOI: 10.1103/PhysRevLett.110.228701 PACS numbers: 89.65.Ef, 47.32.y, 87.15.Zg, 87.23.Cc

Human collective behaviors vary considerably with

social context. For example, lane formation in pedestrian

trafﬁc [1], jamming during escape panic [2], and Mexican

waves at sporting events [ 3] are emergent phenomena that

have been observed in speciﬁc social settings. Here, we

study large crowds (10

–10

attendees) of people under the

extreme conditions typically found at heavy metal concerts

[4]. Often resulting in injuries [5], the collective mood is

inﬂuenced by the combination of loud (130 dB [6]), fast

(blast beats exceeding 300 beats per min) music, synchro-

nized with bright ﬂashing lights, and frequent intoxication

[7]. This variety and magnitude of stimuli are atypical of

more moderate settings and contribute to the collective

behaviors studied here (Fig. 1).

Thousands of videos ﬁlmed by attendees at heavy metal

concerts [8] highlight a collective phenomenon consisting

of 10

–10

participants commonly referred to as a mosh

pit. In traditional mosh pits, the participants (moshers)

move randomly, colliding with one another in an undir-

ected fashion (Fig. 2(a); see Supplemental Material for

video metadata [9]). Mosh pits can form spontaneously

or at the suggestion of the performing band, but in both

cases, no micromanagement of individual actions is gen-

erally involved. Qualitatively, this phenomenon resembles

the kinetics of gaseous particles, even though moshers

are self-propelled agents that experience dissipative

collisions and exist at a much higher density than most

gaseous systems. To explore this analogy quantitatively,

we watched over 10

videos containing footage of mosh

pits on YouTube.com, obtained six that were ﬁlmed from a

suitably high position to provide a clear view of the crowd,

corrected for perspective distortions [10] as well as camera

instability, and used particle image velocimetry (PIV)

analysis [11] to measure the two-dimensional (2D) veloc-

ity ﬁeld on an interpolated grid [Fig. 2(b)].

Video data of mosh pits were used to calculate the

velocity-velocity correlation function c

, where we noted

an absence of the spatial oscillations typically found in

liquidlike systems [Fig. 2(b) inset] [12]. Generally, c

was

well ﬁt by a pure exponential, and for the video used in

Fig. 2, the decay length was 0: 39  0:03 m, which is

approximately human shoulder width. Taken together,

these ﬁndings offer strong support for the analogy between

mosh pits and gases. As a further check, we examined the

2D speed distribution. Previous observations of human

pedestrian trafﬁc and escape panic led us to expect a broad

distribution not well described by simple analytic expres-

sions [2,13]. However, the measured speed distribution in

mosh pits was well ﬁt by the 2D Maxwell-Boltzmann

distribution, which is characterized by the probability

distribution function PDFðvÞ¼ð2v=TÞe

v

and tem-

perature T [Fig. 2(c) and inset] [14]. These observations

present an interesting question: why does an inherently

nonequilibrium system exhibit equilibrium characteristics?

Studies of collective motion in living and complex sys-

tems have found notable success within the framework of

ﬂocking simulations [15–23]. Thus, we use a Vicsek-like

FIG. 1 (color online). This photograph illustrates typical col-

lective behavior found in a mosh pit at heavy metal concerts.

Notice that some attendees are participating (foreground), while

others are not (background). Image courtesy of Ulrike Biets.

PRL 110, 228701 (2013)

PHYSICAL REVIEW LETTERS

week ending

31 MAY 2013

0031-9007=13=110(22)=228701(5) 228701-1 Ó 2013 American Physical Society

model [23] to simplify the complex behavioral dynamics of

each human mosher to that of a simple soft-bodied particle

we dub a mobile active simulated humanoid, or MASHer.

Our model includes two species of MASHers to reﬂect

the typical crowd at heavy metal concerts where we ﬁnd

both active and passive participants (Fig. 1, foreground

and background, respectively) [24]. The ﬁrst species,

referred to as active MASHers repel during collisions,

exhibit self-propulsion, experience ﬂocking interactions,

and are subject to random ﬂuctuations due to environmen-

tal stimuli. These effects are modeled as forces on the ith

MASHer by

repulsion

(



1 



3=2

< 2r

0 otherwise;

(1)

propulsion

¼ ðv

 v

; (2)

flocking

¼ 

j¼0





j¼1



; (3)

noise

¼ ~

: (4)

The Hertzian repulsion force [25] has a strength , and is

determined by the MASHer radius r

, as well as the

distance r

and direction

between MASHers i and j.

A variant of this expression with a 5=2 power law was

tested and found to produce quantitatively similar results.

The self-propulsion force has a strength , is aligned with

the MASHer heading

, and is proportional to the differ-

ence between the current speed v

and the preferred speed

. The ﬂocking force has a strength , and is in the

direction found by vectorially averaging the headings of

the N

MASHers within a distance r

flock

¼ 4r

of MASHer

i. Consistent with previous work [16,22,23], this distance

was ﬁxed in our model so that r

flock

<L, where L is

the system size. This choice minimizes the inﬂuence of

ﬁnite-size effects on the ﬂocking force [15]. Finally, the

random force ~

is a vector whose components 

i;

are

drawn from a Gaussian distribution with zero mean and

standard deviation  deﬁned by the correlation function

h

i;

ðtÞ

i;

ðt

Þi ¼ 2





ðt  t

Þ; the noise is spatially

and temporally decorrelated. Based on observational evi-

dence, the second species in our model, passive MASHers,

prefer to remain stationary and are not subject to ﬂocking

interactions or random forces. Thus, in the appropriate

units, we set v

¼ 0,  ¼ 0, and ~

0 for passive

MASHers. Active MASHers have v

¼ 1, while  and 

were varied to explore the phase space of the model. The

remaining parameters are the same for all MASHers, and

were set to  ¼ 25,  ¼ 1, and r

¼ 1.

We simulated concerts with N ¼ 500 MASHers at a

packing fraction of  ¼ 0:94. Thirty percent of the popu-

lation was active, while the remaining was passive.

Periodic boundary conditions were employed to avoid

edge effects, and numerical integration of

€

repulsion

propulsion

flocking

noise

was performed using the

Newton-Stomer-Verlet algorithm with cell-based neighbor

lists to expedite computation. Initializing the simulation

with uniformly mixed populations, we found that they

spontaneously phase separated with a dense region of

active MASHers conﬁned by passive MASHers. This

occurs generally across parameter space, and appears to

FIG. 2 (color online). (a) Single video frame illustrating a

characteristic mosh pit [8]. (b) The same video image with

overlaid velocity ﬁeld. To facilitate comparisons with (a), this

image is not corrected for perspective distortions. Inset shows

the measured velocity-velocity correlation c

(solid black

circles) as a function of distance r, as well as the best ﬁt to a

pure exponential (black line, R

¼ 0:97). (c) The measured PDF

for speed from the same video (solid black circles), the best ﬁt to

a 2D Maxwell-Boltzmann distribution (black line), and the speed

distribution found in simulations (yellow squares). Inset shows

the best-ﬁt temperature as a function of time illustrating that an

initially ‘‘hot’’ mosh pit ‘‘cools down.’’ Error estimates are in red

for all plots.

PRL 110, 228701 (2013)

PHYSICAL REVIEW LETTERS

week ending

31 MAY 2013

228701-2

be a product of the difference in preferred speeds between

populations (see Supplemental Material [9]). For the

parameter values studied here, this occurs in about 10



ðr

Þ time units and, once formed, remains stable for

greater than 10

ðr

Þ time units.

We explored the model’s phase space by varying 

and  for the active MASHers over the intervals [0,1]

and [0,3], respectively [Fig. 3(a)]. This led to 4:8  10

individual simulations sampled on 4:8  10

grid

points. For each run, we measured the active MASHer

rms angular momentum about their center of mass x

c:m:

ðL=2Þ arctan½ImðAÞ=ReðAÞ, where L ¼ 1:03

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

r

the simulation box size, A ¼

i¼1

expð2ix

=LÞ, N

the number of active MASHers, x

is the x position of the

ith MASHer, and a similar expression holds for y

c:m:

. In the

low-ﬂocking, high-noise limit, we found the angular

momentum was near zero, and upon closer inspection,

discovered a gaslike region [Fig. 3(b)] where MASHers

quantitatively reproduced the statistics found in experi-

mentally observed mosh pits [Fig. 2(c)].

To interpret these results, we note that our model has

three time scales: (i) the ﬂocking time 

flock

¼ v

=,

which can be found by dimensional analysis of Eq (3),

(ii) the noise time 

noise

¼ v

=2

, which can be found

by calculating the amount of time required for noise to

change the correlation function h½v

ð

noise

Þv

ð0Þ

i¼

2



noise

by an amount equal to the characteristic speed

squared, and (iii) the collision time 

coll

¼ 1=ð2r

Þ,

which is the mean-free path ð2r

Þ

1

divided by the speed

. Both noise and collisions tend to randomize motion,

whereas ﬂocking tends to homogenize motion. Thus, when



noise

 

flock

, the statistical motion of the system is

dominated by random forces. The boundary given by this

condition occurs when 

noise

 

flock

, or rather,  

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

=

[Fig. 3(a)]. Similarly, when the 

coll

 

flock

collisions cause disordered motion. This regime is bounded

by   2r

, which is independent of , and for our

choice of parameters is 1; empirically, we ﬁnd   10

2

in agreement with this condition. This demonstrates how a

nonequilibrium system of moshers can have equilibrium

characteristics: random motions induced by collisions or

noise of self-propelled agents over a sufﬁcient time repro-

duce the statistics of classical gases via the central limit

theorem.

Conversely, when 

flock

 

noise

and 

coll

, the ﬂocking

term dominates active MASHer motion. With sufﬁciently

low noise, this limit of the model predicts a highly ordered

vortexlike state [26,27] where MASHers again phase sepa-

rate, but the conﬁned active MASHers move with a large

nonzero angular momentum [Fig. 3(c)]. Remarkably, this

spontaneous phase separation and vortex formation is also

observed at heavy metal concerts where they are conven-

tionally called circle pits (Fig. 4; see Supplemental

Material [9] for video metadata) [8]. In simulations, we

found an even distribution between clockwise (CW) and

counterclockwise (CCW) motion (when viewed from

above) that switches directions at random intervals [28].

However, observations from concerts show 5% ﬂow CW

with the remaining 95% ﬂowing CCW (p<0:001). This

asymmetry is independent of regional conventions in

motor vehicle trafﬁc, as video data were collected from a

variety of countries including the United State of America,

the United Kingdom, and Australia. Though the origin of

this effect is unknown, we speculate it may be related to the

dominant handedness or footedness found in humans, as it

is known to bias turning behaviors [29 ].

The collective behavior described here has not been

predicted on the basis of staged experiments with humans

[30,31], making heavy metal concerts a unique model

system for reliably, consistently, and ethically studying

human collective motion. Currently, the most signiﬁcant

obstacle to further progress is the limited availability of

publicly available high-quality video footage and a general

reluctance among concert organizers to allow ﬁlming at

their events. Nevertheless, further studies in this unique

environment may enhance our understanding of collective

motion in riots, protests, and panicked crowds, as it sheds

light on what collective behaviors become possible when

FIG. 3 (color online). (a) The rms angular momentum of active

MASHers exhibits a disordered gaslike state in the high-noise

low-ﬂocking limit. The model also predicts an ordered vortexlike

state in the low-noise moderate-ﬂocking limit. Dashed white

lines correspond to the bounds of the ﬂocking-dominated

regime. (b) Active MASHers (black) are conﬁned by passive

MASHers (white), and the velocity ﬁeld (red arrows) resembles

that found in actual mosh pits. (c) Active MASHers spontane-

ously self-organize into an ordered vortexlike state. (See

movies 1 and 2 in the Supplemental Material [9].)

PRL 110, 228701 (2013)

PHYSICAL REVIEW LETTERS

week ending

31 MAY 2013

228701-3

traditional social rules are abandoned. Such studies may

lead to new architectural safety design principles and

crowd management strategies that limit the risk of injury

at mass social gatherings [32]. For example, many heavy

metal bands routinely announce during live performances,

‘‘If you see someone fall down in the mosh pit, pick them

back up.’’ This simple rule is known to reduce the risk of

injury by trampling, and if employed in other extreme

social gatherings, would be expected to have similar social

beneﬁts. Similarly, within the MASHer model, we found

that by setting the preferred speed v

¼ 0, all mosh and

circle pit behaviors ceased, suggesting an alternative

approach to real-world crowd safety management.

Heavy metal concerts have the further advantage of

exhibiting a rich variety of collective behaviors such as

(i) the wall of death (moshers split into two groups sepa-

rated by an open space and, when signaled, simultaneously

run at the opposing group leading to a deliberate mass

collision), (ii) pogoing (a locally correlated but globally

decorrelated collective jumping), and (iii) propagating

waves in jammed attendees [33]. In addition to these

broadly deﬁned types of collective motion, there are

further variations that arise when concert organizers focus

on speciﬁc musical subgenres that appeal to niche audien-

ces. For example, hardcore pits , ninja pits, and push pits

are all variants of the traditional mosh pit with their own

unique characteristics that may not, when studied in detail,

be well described by Eqs. (1)–(4). Thus, heavy metal

concerts offer many new opportunities to study the collec-

tive behaviors arising from large groups of humans in

extreme social conditions.

See Ref. [34] for information regarding source codes

used herein.

The photo in Fig. 1 was taken and graciously provided

by Ulrike Biets. J. L. S. and M. B. also thank D. Porter,

L. Ristroph, J. Freund, J. Mergo, A. Holmes, A. Alemi,

M. Flashman, K. Prabhakara, J. Wang, R. Lovelace,

P. McEuen, S. Strogatz, the Cohen Lab, and the Sethna

Group. Fieldwork was independently funded by J. L. S.

*JLS533@cornell.edu

[1] M. Moussaid, D. Helbing, and G. Theraulaz, Proc. Natl.

Acad. Sci. U.S.A. 108, 6884 (2011).

[2] D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys.

Rev. E 75, 046109 (2007).

[3] I. Farkas, D. Helbing, and T. Vicsek, Nature (London) 419,

131 (2002).

[4] R. Walser, Running with the Devil: Power, Gender, and

Madness in Heavy Metal Music (University Press of

New England, Hanover, NH 1993).

[5] T. Janchar, C. Samaddar, and D. Milzman, Am. J. Emerg.

Med. 18, 62 (2000).

[6] A. B. Drake-Lee, J. R. Soc. Med. 85, 617 (1992).

[7] M. S. C. Lim, M. E. Hellard, J. S. Hocking, and C. K.

Aitken, Drug Alcohol Rev. 27, 439 (2008).

[8] Over 10

videos are available on YouTube.com illustrating

mosh pits and circle pits. Some notable examples

include http://youtu.be/5jKU7gdxncE, http://youtu.be/

qkbOyg3NOiE, http://youtu.be/nOHY1YxX5iA, http://

youtu.be/o7w7m4lb2ok, http://youtu.be/l6R7PiISaZw.

[9] See Supplemental Material at http://link.aps.org/

supplemental/10.1103/PhysRevLett.110.228701 for video

metadata, further details of PIV analysis, examples of

phase separation, extended phase diagrams, example

simulation videos, and a copy of the code used in

simulations.

[10] C. Py, E. Langre, B. Moulia, and P. He

mon, Agr. Forest

Meteorol. 130, 223 (2005).

[11] J. K. Sveen and E. A. Cowen, in PIV and Water Waves,

edited by J. Grue, P. L. F. Liu, and G. K. Pedersen

(World Scientiﬁc, Singapore, 2003), Vol. 9, Chap. 1.

[12] N. Ashcroft, Sci. Am. 221, No. 1, 72 (1969).

[13] L. F. Henderson, Nature (London) 229, 381 (1971).

[14] L. Landau and E. Lifshitz, Statistical Physics (Elsevier,

Oxford, 1980), 3rd ed., Chap. 3, Part 1.

[15] I. D. Couzin, J. Krause, R. James, G. Ruxton, and N.

Franks, J. Theor. Biol. 218, 1 (2002).

[16] A. Czirok, E. Ben-Jacob, I. Cohen, and T. Vicsek, Phys.

Rev. E 54, 1791 (1996).

FIG. 4 (color online). The vortexlike state predicted in simu-

lations is also observed at heavy metal concerts, where it is

called a circle pit. (a) Single video frame illustrating two side-

by-side circle pits [8]. (b) The same video image with overlaid

velocity ﬁeld. To facilitate comparisons with (a), this image is

not corrected for perspective distortions. Inset shows the mea-

sured velocity-velocity correlation c

as a function of distance r

(solid black circles, error estimates shown as red band). Note that

is maximally negative at r  6m, corresponding to the

approximate diameter of the leftmost circle pit. Weak oscilla-

tions for r>6m are evident due to long-range correlations

between the two circle pits.

PRL 110, 228701 (2013)

PHYSICAL REVIEW LETTERS

week ending

31 MAY 2013

228701-4

[17] V. Schaller, C. Weber, C. Semmrich, E. Frey, and A.

Bausch, Nature (London) 467, 73 (2010).

[18] N. Leonard, T. Shen, B. Nabet, L. Scardovi, I. D. Couzin,

and S. A. Levin, Proc. Natl. Acad. Sci. U.S.A. 109, 227

(2012).

[19] D. Helbing and P. Molnar, Phys. Rev. E 51, 4282 (1995).

[20] W. Bialek, A. Cavagna, I. Giardina, T. Mora, E. Silvestri,

M. Viale, and A. M. Walczak, Proc. Natl. Acad. Sci.

U.S.A. 109, 4786 (2012).

[21] C. Reynolds, ACM SIGGRAPH Comput. Graph. 21,25

(1987).

[22] T. Vicsek and A. Zafeiris, Phys. Rep. 517, 71 (2012).

[23] T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and

O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).

[24] S. K. You, D. H. Kwon, Y.-i. Park, S. M. Kim, M.-H.

Chung, and C. K. Kim, J. Theor. Biol. 261, 494 (2009).

[25] L. Landau and E. Lifshitz, Theory of Elasticity (Pergamon,

New York, 1986), 3rd ed., Chap. 1.

[26] S. Bazazi, K. S. Pfennig, N. O. Handegard, and I. D.

Couzin, Behav. Ecol. Sociobiol. 66, 879 (2012).

[27] J. Toner, Y. Tu, and S. Ramaswamy, Ann. Phys.

(Amsterdam) 318, 170 (2005).

[28] H. Chen and Z. Hou, Phys. Rev. E 86, 041122

(2012).

[29] C. Mohr, T. Landis, H. S. Bracha, and P. Brugger, Behav.

Neurosci. 117, 1448 (2003).

[30] M. Isobe, D. Helbing, and T. Nagatani, Phys. Rev. E 69,

066132 (2004).

[31] M. Moussaid, D. Helbing, S. Garnier, A. Johansson, M.

Combe, and G. Theraulaz, Proc. R. Soc. B 276, 2755

(2009).

[32] D. Helbing, I. Farkas, and T. Vicsek, Nature (London) 407,

487 (2000).

[33] L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E 79,

021308 (2009).

[34] Source code and a phase diagram generating PYTHON

script are available under the M.I.T. license on github.com

at https://github.com/mattbierbaum/moshpits. An inter-

active JAVASCRIPT version of the simulation is

available at http://mattbierbaum.github.com/moshpits.js.

PRL 110, 228701 (2013)

PHYSICAL REVIEW LETTERS

week ending

31 MAY 2013

228701-5

Here’s a summary of all the emergent behavior that appears when simulating a crowd: #### Mosh Pit $\tau_{flock} > \tau_{noise} \ \& \ \tau_{collision}$ Locally, crowd members move randomly resembling an ideal gas (low coupling, high randomness) ![](https://i.imgur.com/xMYUFAF.png) #### Circle Pit $\tau_{flock} < \tau_{noise} \ \& \ \tau_{collision}$ Locally, crowd members have an organized motion in a circular fashion (moderate coupling and moderate randomness) ![](https://i.imgur.com/MlXc6Mn.png) #### Lanes $\tau_{flock} <{}< \tau_{noise} \ \& \ \tau_{collision} $ Locally, crowd members move in a organized motion with a clear linear direction (strong coupling and low randomness) ![](https://i.imgur.com/RSMhqJ4_d.webp?maxwidth=760&fidelity=grand) It’s important to note that most of this work was done based on simulations and with very limited access to effective videos. It would be interesting to try and recreate experiments in a control environment to study these crowd behaviors. Notice a clear phase transition from a gas like behavior and vortex formation Studies like this that explore emergent behaviors in crowds could be useful when thinking about better social engineering strategies to mitigate problems in potentially dangerous situations like panicked escapes from crowded environments or high-volume pedestrian traffic situations. An ideal gas is a theoretical gas composed of many randomly moving point particles in which the interactions are regarded as point-like collisions. The Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, defines the distribution of speeds for an ideal gas at a certain temperature. ## TL;DR In this paper the authors analyzed videos on YouTube of mosh pits and conducted a particle image velocimetry analysis (PIV) to study the distribution of velocities and found out that mosh pits behave like an ideal gas. They then built computer simulations to map the parameter space and discovered that modeling crowds using a simple repulsion, propulsion, flocking and noise force terms would result in multiple emergent behavior: mosh pit, circle pit and lanes!

Comments

Products

Project