Swarming and Music
Transcript of Swarming and Music
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i xv j
i S (i)
d
(x, v)
i S
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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
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pi
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n
n − 1
d
f
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S (1 − 3) H p
H (1 − 3)E
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P
Q f
Q
E
E p
P P f
x H
p f
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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)
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t τ
vmax ∆τ
∆τ
x
f
H
p
H
H
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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
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→ → →
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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
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x3
x1
aattri = C
X
all perceived attractors
( p − xi)
C
2N d
x2 ∼ 1
∆t
x2
x4
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arepuli = K
X
all perceived particles
(xi − xj )
(xi − xj)3
K
P Qf
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x1 x3
H
H A
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P Df
P f
Q
P Qf
Q f
P
α
Q
1
120 BP M 1
60 BP M
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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}
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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
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n
n → n − 1 → n − 2
n → n + 1 →
n + 2
f
f
f.
f
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P Qf
x f (x, α)α
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