124
4. SIMULATING GROWTH AND FORM
a parabolic shape. As a consequence, there exists little probability of growth
in the depleted region .
The absorption patterns shown in Fig. 4.29 show an asymmetry in the
absorption of nutrients at the boundary nodes of the aggregates for increasing
Pe numbers. For the diffusion-limited case (Fig. 4.29a) the highest degree of
absorption is found at the tips of the object, while near the center hardly any
nutrient is being absorbed. In Fig. 4.29b the highest amount of absorption is
found at the upstream side of the object . This corresponds to the observations
done in experimental work on the absorption of food particles by the stony
coral Madracis mirabilis (see Fig. 2.5), where the highest amount of food
particle capture was found at the upstream side ofthe colony (see Fig. 2.6). In
Table 4.3 it can be seen that the average absorption aincreases for increasing
Pe numbers. The absorption pattern characteristic of the diffusive regime
changes into a more slowly decaying distribution. In other words, the flow
results in a more even distribution of nutrient in boundary nodes. This
is illustrated by the decrease in the measure Dabs of the uniformity of the
nutrient distribution. Asa result the probability that boundary sites are added
to the aggregate becomes more equal, which accounts for the increasing
degree of compactness of the aggregate .
When comparing Figs. 4.30 and 4.31, it can be observed that the added
part in Fig. 4.31 (visualized in white) "hides" the previous growth stages, so
all boundary sites seem to have a more or less equal probability of being
added to the aggregate, while in Fig. 4.30 the "trunk" of the object remains
visible and growth occurs only at the tips of the object. A gradual increase of
compactness is demonstrated in Fig. 4.26 and by a decrease of both D box and
the ratio R of the total sink nodes to the total cluster size in Table 4.3for an increasing influence of hydrodynamics. This gradual increase of compactness
corresponds qualitatively to the observations made in stony corals, hydrocorals, and sponges, where growth forms gradually transform from a compact
shape, under conditions exposed to water movement, into a thin-branching
one under sheltered conditions. Qualitatively this corresponds to the ~ox
measurements, estimated for the plane-filling properties of the projections
of the growth forms, analyzed in Sect. 3.3.2. The other morphological properties, based on the skeleton of the object, cannot easily be compared. In the
aggregation model, growth is represented by the addition of discrete sites in
a three-dimensional lattice, which is a substantial simplification of the actual
growth process. The actual growth process in many sponges, stony corals,
and hydrocorals (see also Fig. 1.4) consists of adding layers of material (varying in thickness) on top of the preceding growth stage, and not the addition of
particles. In the section on accretive growth (Sect. 4.6) we will try to develop
a growth model, based on surface normal deposition, which comes closer
to the actual growth process . An accretive growth model, in which layers of
material are constructed on top of the previous layers and where the local
thickness is determined by the local amount of absorbed nutrients or light intensity, also offers possibilities for a quantitative morphological comparison
of simulated and actual growth forms as was discussed in Sect. 3.3.2.
In the bidirectional flow model several other simplification are made. In
many stony corals, for example the species Pocillopora damicornis,photosynthesis represents a major energy input. Furthermore, there is no mechanism
present in the aggregation model for nutrient accumulation at some distance
from the object and there are no effects of erosion included in the model.
4. SIMULATING GROWTH AND FORM
a parabolic shape. As a consequence, there exists little probability of growth
in the depleted region .
The absorption patterns shown in Fig. 4.29 show an asymmetry in the
absorption of nutrients at the boundary nodes of the aggregates for increasing
Pe numbers. For the diffusion-limited case (Fig. 4.29a) the highest degree of
absorption is found at the tips of the object, while near the center hardly any
nutrient is being absorbed. In Fig. 4.29b the highest amount of absorption is
found at the upstream side of the object . This corresponds to the observations
done in experimental work on the absorption of food particles by the stony
coral Madracis mirabilis (see Fig. 2.5), where the highest amount of food
particle capture was found at the upstream side ofthe colony (see Fig. 2.6). In
Table 4.3 it can be seen that the average absorption aincreases for increasing
Pe numbers. The absorption pattern characteristic of the diffusive regime
changes into a more slowly decaying distribution. In other words, the flow
results in a more even distribution of nutrient in boundary nodes. This
is illustrated by the decrease in the measure Dabs of the uniformity of the
nutrient distribution. Asa result the probability that boundary sites are added
to the aggregate becomes more equal, which accounts for the increasing
degree of compactness of the aggregate .
When comparing Figs. 4.30 and 4.31, it can be observed that the added
part in Fig. 4.31 (visualized in white) "hides" the previous growth stages, so
all boundary sites seem to have a more or less equal probability of being
added to the aggregate, while in Fig. 4.30 the "trunk" of the object remains
visible and growth occurs only at the tips of the object. A gradual increase of
compactness is demonstrated in Fig. 4.26 and by a decrease of both D box and
the ratio R of the total sink nodes to the total cluster size in Table 4.3for an increasing influence of hydrodynamics. This gradual increase of compactness
corresponds qualitatively to the observations made in stony corals, hydrocorals, and sponges, where growth forms gradually transform from a compact
shape, under conditions exposed to water movement, into a thin-branching
one under sheltered conditions. Qualitatively this corresponds to the ~ox
measurements, estimated for the plane-filling properties of the projections
of the growth forms, analyzed in Sect. 3.3.2. The other morphological properties, based on the skeleton of the object, cannot easily be compared. In the
aggregation model, growth is represented by the addition of discrete sites in
a three-dimensional lattice, which is a substantial simplification of the actual
growth process. The actual growth process in many sponges, stony corals,
and hydrocorals (see also Fig. 1.4) consists of adding layers of material (varying in thickness) on top of the preceding growth stage, and not the addition of
particles. In the section on accretive growth (Sect. 4.6) we will try to develop
a growth model, based on surface normal deposition, which comes closer
to the actual growth process . An accretive growth model, in which layers of
material are constructed on top of the previous layers and where the local
thickness is determined by the local amount of absorbed nutrients or light intensity, also offers possibilities for a quantitative morphological comparison
of simulated and actual growth forms as was discussed in Sect. 3.3.2.
In the bidirectional flow model several other simplification are made. In
many stony corals, for example the species Pocillopora damicornis,photosynthesis represents a major energy input. Furthermore, there is no mechanism
present in the aggregation model for nutrient accumulation at some distance
from the object and there are no effects of erosion included in the model.