126
4. SIMULATING GROWTH AND FORM
to the suspended material in the immediate environment, and is relatively
higher compared with the flattened sites of the growth form.
As was discussed in Sect. 4.5.1 water flow has a strong influence on the
distribution of food particles in the immediate environment of suspension
feeders and on the resulting morphology of the sessile suspension feeder. In
branching sessile organisms growth forms emerge which have a roughly radial symmetry (see also Sect. 2.2.4 and Fig. 2.39a and b) or show a tendency
to develop a flattened growth form. In the latter case most branches will develop in a plane perpendicular to the governing flow direction. Furthermore
there is a strong influence on the overall degree of compactness of the organism, which can be observed in sessile organisms from various taxonomical
groups: in general thin-branching forms tend to be formed in the absence of
water movement, while more compact shapes develop when the influence of
water movement increases. Local food particle absorption patterns related to
the direction and the velocity of the flow, depletion zones surrounding the organism, and micro flowpatterns in branching organisms have important consequences for the growth process and the resulting morphology in organisms
where suspension feeding represents a significant part of the energy intake.
In the section on the regulation of the growth process of the stony coral
Stylophora pistillata (Sect. 2.2.4), it was stated that this coral forms colonies
with a roughly radial symmetry and that the colonies are approximately
spherical. A remarkable property of the growth in Stylophora pistillata is that
branches never fuse. There is a very regular spacing between the branches;
a similar phenomenon can be observed in Figs. 2.5,3-17, and 3.18 showing the
stony coral Madracis mirabilis. More or less spherical colonies are formed,
where branches do not fuse and where the branch spacing (br_spacing, see
also Sect.3 .3.2) is remarkably constant. In Rinkevich and Loya (1985a) this
phenomenon was explained by proposing a chemical signal which regulates
the growth pattern. In their observations, done in field experiments with
Stylophora pistillata, it was demonstrated that as soon as branches grow towards the other branches, a buffer zone seems to be formed in the immediate
vicinity of each branch. Growth of branches in this region is suppressed or
the growth direction is changed (see also Fig. 2.39). In the paper by Rinkevich and Loya (1985a) it is proposed that a chemical agent ("isomone") which
suppresses the growth process is emitted by the tissue cells and secreted into
the water.
In this section several types of models of accretive growth will be discussed, to give an overview of the variety of morphologies which can be
produced with this model. The deposition in a surface normal accretive
growth process is modeled using a geometrical model. The layers formed in
the growth process are represented as layers consisting of triangulated meshes
constructed on top of each other. The thickness of a new layer, measured along
the surface normal of the previous layer, is determined by a growth function . Several types of models of accretive growth can be constructed by using
different types of growth functions.
In the first model, discussed in Sect. 4.6.3, the distribution of growth velocities over a tip of an organism with accretive growth is approximated with
a mathematical function. The distribution can be obtained from, for example, figures as shown in Figs. 1.4or 2.17. In this first model the approximation
of the growth velocity distribution is combined with the effect of the local
amount of contact with the environment. The local amount of contact with
4. SIMULATING GROWTH AND FORM
to the suspended material in the immediate environment, and is relatively
higher compared with the flattened sites of the growth form.
As was discussed in Sect. 4.5.1 water flow has a strong influence on the
distribution of food particles in the immediate environment of suspension
feeders and on the resulting morphology of the sessile suspension feeder. In
branching sessile organisms growth forms emerge which have a roughly radial symmetry (see also Sect. 2.2.4 and Fig. 2.39a and b) or show a tendency
to develop a flattened growth form. In the latter case most branches will develop in a plane perpendicular to the governing flow direction. Furthermore
there is a strong influence on the overall degree of compactness of the organism, which can be observed in sessile organisms from various taxonomical
groups: in general thin-branching forms tend to be formed in the absence of
water movement, while more compact shapes develop when the influence of
water movement increases. Local food particle absorption patterns related to
the direction and the velocity of the flow, depletion zones surrounding the organism, and micro flowpatterns in branching organisms have important consequences for the growth process and the resulting morphology in organisms
where suspension feeding represents a significant part of the energy intake.
In the section on the regulation of the growth process of the stony coral
Stylophora pistillata (Sect. 2.2.4), it was stated that this coral forms colonies
with a roughly radial symmetry and that the colonies are approximately
spherical. A remarkable property of the growth in Stylophora pistillata is that
branches never fuse. There is a very regular spacing between the branches;
a similar phenomenon can be observed in Figs. 2.5,3-17, and 3.18 showing the
stony coral Madracis mirabilis. More or less spherical colonies are formed,
where branches do not fuse and where the branch spacing (br_spacing, see
also Sect.3 .3.2) is remarkably constant. In Rinkevich and Loya (1985a) this
phenomenon was explained by proposing a chemical signal which regulates
the growth pattern. In their observations, done in field experiments with
Stylophora pistillata, it was demonstrated that as soon as branches grow towards the other branches, a buffer zone seems to be formed in the immediate
vicinity of each branch. Growth of branches in this region is suppressed or
the growth direction is changed (see also Fig. 2.39). In the paper by Rinkevich and Loya (1985a) it is proposed that a chemical agent ("isomone") which
suppresses the growth process is emitted by the tissue cells and secreted into
the water.
In this section several types of models of accretive growth will be discussed, to give an overview of the variety of morphologies which can be
produced with this model. The deposition in a surface normal accretive
growth process is modeled using a geometrical model. The layers formed in
the growth process are represented as layers consisting of triangulated meshes
constructed on top of each other. The thickness of a new layer, measured along
the surface normal of the previous layer, is determined by a growth function . Several types of models of accretive growth can be constructed by using
different types of growth functions.
In the first model, discussed in Sect. 4.6.3, the distribution of growth velocities over a tip of an organism with accretive growth is approximated with
a mathematical function. The distribution can be obtained from, for example, figures as shown in Figs. 1.4or 2.17. In this first model the approximation
of the growth velocity distribution is combined with the effect of the local
amount of contact with the environment. The local amount of contact with