XIV
TABLE OF CONTENTS
Chapter 4 Simulating Growth and Form
91
4.1
L-systems
91
4.1.1
Introduction to Modeling Using L-systems
91
4.1.2
Examples ofL-systems for Modeling Seaweed. .. . ........... . . .. 94
4.2
Example of a Simple Model of Plast icity
in Algal Morphology
97
4.3
Modeling Fluid Flow Using Lattice Gases
and the Lattice Boltzmann Model
99
4.3.1
Cellular Automata as Models for Fluid Flow
100
4.3.2
Transport, Erosion, Deposition, and Hydrodynamic Forces
105
4.3.3
Transport and Sedimentation
108
4.4
A Laplacian Model of Branching Growth
109
4.4.1 Laplacian Growth
109
4.4.2 The Numerical Model
110
4.4.3 Model Results
112
4.5
Growth by Aggregation
114
4.5.1
Morphological Plasticity and the Influence
of Hydrodynamics
114
4.5.2
Modeling the Nutrient Distribution
115
4.5.3
Growth by Aggregation in a Monodirectional Flow
116
4.5.4
Growth by Aggregation in a Bidirectional (Alternating) Flow . . 119
4.5.5
Comp arison Between the Range of Aggregates
and the Growth Forms
123
4.6
Accretive Growth
125
4.6.1 Surface Normal Deposition in Marine Sessile Organisms
125
4.6.2 A Model of Surface Normal Accretive Growth
127
4.6 .3 Accretive Growth Using an Approxim ation
of Actual Deposition Velocities
and the Amount of Contact with the Environment
128
4.6.4 A Model of Accretive Growth Driven by the Local Amount
of Available Nutrient and the Influence of Hydrodynamics ..... 130
4.6 .5 A Model of Accret ive Growth
Driven by Local Light Intensities
137
4.6. 6 A Model of Accretive Growth
Driven by Local Nutrient Availability
and Regulated by a Growth-Suppressing Isomone
139
4.6 .7 A Comparison Between the Accretive Model
and the Growth Forms
139
4.7
Gastrovascular Dynamics of Hydractiniid Hydrozoans ......... 144