A QUICK GUIDE TO FRACTAL BEHAVIOUR
Structure function:
<(
D
S
t
)
q
> = <|S(t+
t
)-S(t)|
q
>
Scaling:
<(
D
S
t
)
q
> =
<(
D
S
T
)
q
>(
t
/T)
z
(q)
z
(q) is the scaling exponent
Monofractal:
z
(q) is linear
Multifractal:
z
(q) is non-linear
Universal multifractal:
z
(q)=qH-[C
1
/(
a
-1)](q
a
-q)
b
=1+
z
(2)