Swarming and Music

8/19/2019 Swarming and Music

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i xv j

i S (i)

d

(x, v)

i S



ai = 1m f (S (i), α)

vi(t + 1) = vi(t) + ai

vi(t + 1) = min(vi(t), vmax)

xi(t + 1) = xi(t) + vi(t + 1)

dt = 1 S (i) i

ai f

S (i) α m

S (i)

xi

xj

ai = xj − xi

|xj − xi|

ai

ai = C ( pi − xi)

C pi

i i



pi





n

n − 1

d

f





S (1 − 3) H p

H (1 − 3)E



P

Q f

Q

E

E p

P P f

x H

p f



Q x

q Q

P Qf

P Q f

f

x(t + 1) = f (x(t), v(t), p(t), α)

{x, v} p = P (E )α

α

α

α

α1 = α1(α2, α3 . . .) α = α(x, v, p)α

αj

α

x(t) → x(t + 1)



t τ

vmax ∆τ

∆τ

x

f

H

p

H

H



a

∆t

f

∆tevent

nchord

nseq

s

N

P

P

P a f

P

p

N

p5−N +N

s s = 1N

N

Q S N N

{a, ∆t, f, ∆tevent} a S N

x1



→ → →



x2−4

S N

x̄ =X

all particles

x

Q x̄5−7

S N nchord = x̄5

∆t nchord S N

nseq = x̄6

S N

{a, ∆

t, ∆

tevent} x̄7S N

f

P Q

f

p



x3

x1

aattri = C

X

all perceived attractors

( p − xi)

C

2N d

x2 ∼ 1

∆t

x2

x4



arepuli = K

X

all perceived particles

(xi − xj )

(xi − xj)3

K

P Qf



x1 x3

H

H A



P Df

P f

Q

P Qf

Q f

P

α

Q

1

120 BP M 1

60 BP M



P Q

E H

f Q

P Qf

P new

E P new E

H

Qnew

Qnew = P −1new

nchord nseq

vmax

vmax

vmax = 0vmax

P

vmax

P

{. . . , ei, . . . , ej} ejN {ei, . . . , ej}, j = i + N {i → j}

s({i → j}, {k → l}) {i → j} N

{k → l}



s({i → j}, {k → l}) = 1N

N −1X

n=0

c(ei+n, ek+n)

c(ei, ej )[0, 1]

ei ej

c(ei, ej ) ei = ej

n n ≤ N N

s({i → j}, {k → l}) k = i − 1, i − 2, . . . , i − N N

s = max

k

s({i → j}, {k → l}))

s

P

P

p p7 = (1 − s) X X H = [0, X ]7

H

x7 Q

vmax = x̄7

V

X

V

x̄ = 0

s x̄

H

Q vmax

vmax 7

p7



n

n → n − 1 → n − 2

n → n + 1 →

n + 2

f

f

f.

f



P Qf

x f (x, α)α





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Swarming and Music