fractal structures janez podhostnik
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f (x) =∞n=0
an cos(bnπx)
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X
S ⊂ X
d ∈ [0,∞)
d S
C dH (S ) := inf
i
rdi : S ri > 0
.
X
dimH(X ) := inf {d ≥ 0 : C d
H (X ) = 0}.
N (r) r X r N (r)
r
N (r)
X
d N (r) 1rd
N ()
dim = lim→0
(log N ()
log 1
)
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[0, 1]
13
k
N ()
2k
dim = log2k
log3k =
log 2
log 3 = 0.6309
N
N
N 2
N 2
N
N 3 N
dim = log(
)
log (
)
dim = log 2log 3
log 4
log 9 = log 2
2
log 32 = log 2
log 3
log 3
log 2
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c
|c| < 2
zn+1 = z2n
+ c z0 = 0 c
z0 b
2.97
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V
[0, 1]
H = − ∂ 2
∂x2
ψn(x, t) =√
2sin knxe−itE n
kn = nπ
E n = n2π2
kn = E n
0 <
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t = 0.032
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