Fractals have fascinated computer scientists, biologists, and laypeople since the publication of Mandelbrot’s book [1]. Relatively simple computer programs can generate branching structures that have a remarkable resemblance to structures in plants, the human lung, or the growth of coral reefs. Nevertheless, some skepticism remains as to whether these structures have more than a superficial resemblance to the growth of living organisms. This book makes it clear that at least for two marine organisms, corals and sponges, fractal models are not only suggestive but have predictive value. The emphasis is on the development of simulation models, which enable the study of the growth process and the influence of environmental parameters on the particular patterns of growth.

The book is important for two reasons. First, it provides an approach to the development of fractal simulation models, which are useful for a wide variety of branching structures in nature (not only corals and sponges). Second, since corals are endangered in several parts of the world, the models described here provide a predictive tool to study the effects of water movement, light, pollutants, nutrient supply, and other environmental variables.

The book is the outcome of the author’s doctoral research at the University of Amsterdam, followed by a fellowship at the University of Calgary. Kaandorp is formally trained in both biology and computer science, and this dual background is evident throughout the book. He clearly knows a great deal about corals and sponges. While these organisms are used for illustration throughout, most of the emphasis is on modeling the growth of various forms, in both two and three dimensions. Mathematical models and pseudocode algorithms are used to provide generality.

Following a brief introduction to the subject in chapter1, the author devotes chapter 2 to a review of methods for modeling the growth of biological objects. One of the earliest models of morphogenesis (pattern formation) is due to  Turing,  who published a chemical model in 1952. Starting with this reaction diffusion model, the author reviews various iterative processes leading to fractals, as well as  Lindenmayer’s  model, which uses formal languages to generate objects. Various methods of obtaining fractal representations are presented, including the author’s own contribution, which generates objects by geometric constructions. Geometric rules that can be used for the iterative construction of a variety of growth shapes are presented, using base elements, “initiator” structures, and “generator” algorithms. The algorithms are illustrated with both black-and-white and color pictures of the resulting forms.

Chapter 3 presents various methods for simulating two-dimensional models of marine organisms, specifically corals and sponges. While chapter 2 is quite general, this chapter is highly specific to these animals, which are reputed to have a relatively simple growth process, so that it is relatively easy to obtain the geometric production rules needed to simulate it. Following a review of the forms of these organisms seen in nature, the book describes the models used for simulation. Chapter 4 then compares the various models and the geometric forms they produce, describes simulation experiments, and discusses experimental verification. In order to test the predictive capability of the models, various experiments with a type of coral were performed, in which the normal growth process was interrupted by transplantation, and the effects of various parameters could be studied. Three-dimensional models of growth forms are described in chapter 5. The final chapter describes other potential applications of these models in ecological studies. Since environmental parameters strongly influence the way in which these organisms grow, the models can be used for ecological monitoring as well as for scientific studies of morphogenesis.

This beautifully illustrated book provides geometric methods for the generation of fractal models, as applied to the growth of corals and sponges. While the author indicates that the methods are applicable to other living systems, this extension is left to the reader. Nevertheless, the book is a major contribution to the field, in that it provides not only algorithms but experimental evidence that fractals are not just a mathematical curiosity, but also tools for the serious study of branching growth forms in nature.