Seuront L. Fractals and Multifractals in Ecology and Aquatic Science
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344 Index
Zero slope
criterion, 237
procedure, 234–237
Zipf exponent, 186
Zipf’s law
basis of, 155
competing power laws, 168
contaminated power laws, 165
deterministic processes, 165
diagnose ecosystem complexity, 176
as diagnostic tool to assess ecosystem complexity,
161–177
distance between, 188–189
generalized, 158–160
human communication, and principle of least effort, 155
information, and entropy, 156–158
monotonic, 165
n-gram entropy and n-gram redundancy, 193–199
n-tuple Zipf’s law, 189–193
periodic trends, 165
power laws
contaminated by external (white) noise, 165
contaminated by internal (process) noise, 168
pure, 165
random processes, 161
two-dimensional patterns, 177
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Figure 1.7 South Australian landscapes, with (A) and without (B) anthropogenic inuences. Both pictures
were taken from an altitude of 20 km.
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Figure 2.3 Nested structure perceptible in the geometry of clouds. At increasing resolution, the local and
global structures remain very similar.
A B
C D
AB
CD
Figure 1.9 Contrast existing between the geometry of a man-made surface, a brick wall (A) and (B) the
bark patterns of the white g (Ficus virens), (C) the English oak (Quercus robur), and (D) the cotton palm
(Washingtonia lifera).
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A B
C D
AB
CD
Figure 3.11 Salt-marsh environments where H. haswellianus burrow morphology was investigated in (A)
Goolwa, (B) Torrens Island, (C) Middle Beach, and (D) Port Noarlunga. (Courtesy of G. Katrak, Flinders
University, Australia.)
A BAB
Figure 4.14 The Australian nectar-feeding passerines (A) New Holland honeyeater (Phylidonyris novae-
hollandiae) and (B) red wattlebird (Anthochaera carunculata).
Figure 3.27 Classical view of the pristine waters of the ocean interior (A) compared to a more realistic view
illustrating the occurrence of marine snow particles (B).
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Figure 7.9 Spatial isotropy of fractal dimension estimates. From a two-dimensional pattern of microphy-
tobenthos biomass (recorded in the Bay of Somme, April 25, 2002; Seuront and Spilmont, unpublished data)
one-dimensional fractal dimensions have been estimated for horizontal and vertical sections (A) and different
diagonal sections (B) of the initial pattern. The resulting patch-intensity dimensions (see Section 5.2) cannot
be regarded as signicantly different from the two-dimensional estimate (C; p > 0.05 ), showing the isotropic
character of the initial distribution. The dashed and dotted lines represent the two-dimensional patch-intensity
dimension and its 95% condence interval, respectively.
AB
Chl.
(mg.m
‒
2
)
C
D
pi
Transects
141312
1.70
1.69
1.68
1.67
1.66
1.65
1.64
1.63
1.62
1.61
1.60
1110987654321
15
10
5
0
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