Fractal Modelling
Growth and Form in Biology
Published on 12. April 1994
Book
Hardback
XIII, 209 pages
978-3-540-56685-4 (ISBN)
Description
New developments in computer science, biology, mathematics and physics offer possibilities to obtain deeper understanding of growth and forms of organisms. It is now possible to carry out simulation experiments in which the growth process can be simulated in virtual computer objects. In this book, methods from fractal geometry are applied to model growth forms. As a case study, a type of growth process is used which can be found among various taxonomic classes of organisms such as sponges and corals. The growth of these organisms is simulated with 2D and 3D geometrical objects. The models presented in the book provide a rendering method for natural objects which is based on the actual growth process. The models can be used, for example, to understand the amazing variety of forms to be found in a coral reef. Models which mimic the growth of forms and the environmental influence on the growth process are also useful for ecologists. A combination of simulation models and the actual growth forms can be used to detect the effects of slow changes in the environment.
More details
Edition
1994 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Professional/practitioner
Illustrations
XIII, 209 p.
Dimensions
Height: 285 mm
Width: 215 mm
Thickness: 19 mm
Weight
888 gr
ISBN-13
978-3-540-56685-4 (9783540566854)
DOI
10.1007/978-3-642-57922-6
Schweitzer Classification
Other editions
Additional editions
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12/2012
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10/2012
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Persons
Content
1 Introduction.- 1.1 Structure of the Book.- 2 Methods for Modelling Biological Objects.- 2.1 Reaction Diffusion Mechanisms.- 2.2 Iteration Processes and Fractals.- 2.3 Generation of Objects Using Formal Languages.- 2.4 Diffusion Limited Aggregation Models.- 2.5 Generation of Fractal Objects Using Iterated Function Systems.- 2.6 Iterative Geometric Constructions.- 2.7 A Review of the Methods.- 3 2D Models of Growth Forms.- 3.1 Modular Growth.- 3.2 Radiate Accretive Growth.- 3.3 Growth Forms of Modular Organisms and the Physical Environment.- 3.4 Description of the Internal Architecture of the Autotrophic Example: Montastrea annularis.- 3.5 Description of the Internal Architecture of the Heterotrophic Example: Haliclona oculata.- 3.6 An Iterative Geometric Construction Simulating the Radiate Accretive Growth Process of a Branching Organism.- 3.7 A Model of the Physical Environment.- 3.8 Conclusions and Restrictions of the 2D Model.- 3.9 List of Symbols Used in this Chapter.- 4 A Comparison of Forms.- 4.1 A Comparison of a Range of Forms.- 4.2 An Experimental Verification of the Model.- 4.3 Conclusions.- 5 3D Models of Growth Forms.- 5.1 Constructions in Space, a 3D Modelling System for Iterative Constructions.- 5.2 Description of an Organism with Radiate Accretive Growth and a Triangular Tessellation of the Surface.- 5.3 Representation of a Triangular Tessellation.- 5.4 Representation of a Multi-Layer Triangular Tessellation.- 5.5 The Lattice Representation of a Volume Tessellated with Triangles.- 5.6 An Iterative Geometric Construction Simulating the Radiate Accretive Growth Process of a Branching Organism.- 5.7 Conclusions and Restrictions of the Presented 3D Models.- 5.8 List of Symbols Used in Sects. 5.3 to 5.7.- 6 Final Conclusions.- 6.1 The 2D and 3D Simulation Models.- 6.2 Application of the Simulation Models in Ecology.- References.