Neue interdisziplinäre Entwicklungen wie fraktale Geometrie, Bilderzeugung und 3D-Modellierung machen Furore in Informatik, Mathematik, Biologie und Physik. Sie ermöglichen beispielsweise die experimentelle Simulation von Wachstum und Formen biologischer Organismen an virtuellen Objekten. Die beschriebenen und mit vielen eindrucksvollen Farbbildern demonstrierten Modelle, z.B. von Korallen und Meeresschwämmen, geben auch Einblick in die Wirkung von Umweltveränderungen.
Neue interdisziplinäre Entwicklungen wie fraktale Geometrie, Bilderzeugung und 3D-Modellierung machen Furore in Informatik, Mathematik, Biologie und Physik. Sie ermöglichen beispielsweise die experimentelle Simulation von Wachstum und Formen biologischer Organismen an virtuellen Objekten. Die beschriebenen und mit vielen eindrucksvollen Farbbildern demonstrierten Modelle, z.B. von Korallen und Meeresschwämmen, geben auch Einblick in die Wirkung von Umweltveränderungen.
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.
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.
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