The relationship between growth and form is one of the most exciting problems in biology. The complexity of developmental processes that transform a seed into an adult tree or a fertilized egg into an animal is difficult to comprehend and defies traditional mathematical descriptions. Their limitations led Benoit Mandelbrot to the discovery of fractals: the intricate geometric objects more suitable for representing irregular forms of nature than figures of Euclidean geometry. Mandelbrot observed that many fractals could be obtained using a strikingly simple construction invented in 1905 by Helge von Koch and consisting of repetitive substitutions of given geometric figures by sets of other figures. In 1968, Aristid Lindenmayer proposed a similar mechanism as a mathematical model of the development of multicellular organisms. In this case, cell divisions were viewed as substitutions of the mother cells by their children. The analogy between the substitution of geometric figures and the division of cells related fractals to developmental biology.
In this book, Jaap Kaandorp applies mathematical models and computer simulations rooted in fractals to explore the relationship between growth and form in marine sessile organisms: corals and sponges. The sophistication of the models progresses from simple geometric abstractions to comprehensive models of specific organisms found in nature. Commendably, Kaandorp emphasizes the predictive power of the models as the essential criterion of their practical value. One interesting application is biomonitoring, in which a mathematical model is used to establish the relationship between the shape of an organism and its environment. This relationship makes it possible to use the shape of a growing organism as an indicator of environmental conditions. The purpose may range from pollution control to the study of long-term climatic changes.
Most of the book is devoted to the description of Kaandorp's original results obtained in the scope of his Ph.D. research at the University of Amsterdam, followed by a fellowship at the University of Calgary.
