3. Measuring Growth and Form
A
morphological analysis of the growth forms of marine sessile organisms is an important prerequisite for research on these organisms.
A quantitative morphological analysis is required in studies on the morphological plasticity in marine sessile organisms. To verify simulation models
a morphological comparison between actual and simulated forms is essential. In this chapter we will discuss a number of methods suitable for the
quantitative morphological comparison of (branching) forms. In the first
two sections methods will be discussed for computing ratios and fractal dimensions in two-dimensional images of branching structures. The
third section focuses on the morphological analysis of two-dimensional
images of growth forms sampled along environmental gradients. In the
fourth section some preliminary results are presented for the morphological analysis of three-dimensional images of simulated and actual growth
forms.
3.1 Metrics for Branching Networks
Networks are a universal feature of complex systems and structures in the
world around us. The task of a network is often crucial : cardiovascular systems supply nutrients, central nervous systems carry biological information,
social and business networks link people, and river networks transport water
and chemicals, patterning the earth's topography. In the design of biological
organisms we find networks in both body shapes and internal systems. In
seeking to understand networks, we evidently need a way of quantifying network structure and in the present section we will discuss some fundamental
network metrics.
A significant portion of important networks are purely branching networks, i.e. they contain no closed circuits and there is only one path along
the network between any two points . The archetypal example of a branching network is a tree : a trunk rooted on a surface that repeatedly shoots off
branches as it extends upwards with each branch possessing a similar form
to the overall structure.
Of course, we find an abundant source of branching networks in the
forms of seaweeds, sponges, and corals. A natural question is how do we begin
to quantitatively compare and distinguish the branching patterns of these
organisms? What are the relevant metrics? To this end, we consider a simple
method of describing branching networks and then two complementary
metrics for such networks.
J. A. Kaandorp et al., The Algorithmic Beauty of Seaweeds, Sponges and Corals
© Springer-Verlag Berlin Heidelberg 2001
A
morphological analysis of the growth forms of marine sessile organisms is an important prerequisite for research on these organisms.
A quantitative morphological analysis is required in studies on the morphological plasticity in marine sessile organisms. To verify simulation models
a morphological comparison between actual and simulated forms is essential. In this chapter we will discuss a number of methods suitable for the
quantitative morphological comparison of (branching) forms. In the first
two sections methods will be discussed for computing ratios and fractal dimensions in two-dimensional images of branching structures. The
third section focuses on the morphological analysis of two-dimensional
images of growth forms sampled along environmental gradients. In the
fourth section some preliminary results are presented for the morphological analysis of three-dimensional images of simulated and actual growth
forms.
3.1 Metrics for Branching Networks
Networks are a universal feature of complex systems and structures in the
world around us. The task of a network is often crucial : cardiovascular systems supply nutrients, central nervous systems carry biological information,
social and business networks link people, and river networks transport water
and chemicals, patterning the earth's topography. In the design of biological
organisms we find networks in both body shapes and internal systems. In
seeking to understand networks, we evidently need a way of quantifying network structure and in the present section we will discuss some fundamental
network metrics.
A significant portion of important networks are purely branching networks, i.e. they contain no closed circuits and there is only one path along
the network between any two points . The archetypal example of a branching network is a tree : a trunk rooted on a surface that repeatedly shoots off
branches as it extends upwards with each branch possessing a similar form
to the overall structure.
Of course, we find an abundant source of branching networks in the
forms of seaweeds, sponges, and corals. A natural question is how do we begin
to quantitatively compare and distinguish the branching patterns of these
organisms? What are the relevant metrics? To this end, we consider a simple
method of describing branching networks and then two complementary
metrics for such networks.
J. A. Kaandorp et al., The Algorithmic Beauty of Seaweeds, Sponges and Corals
© Springer-Verlag Berlin Heidelberg 2001