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Fractal modelling : growth and form in biology

Author: Jaap A Kaandorp; Przemyslaw Prusinkiewicz
Publisher: Berlin : Springer, ©1994.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

In this book, methods from fractal geometry are applied to model growth forms, taking as a case study a type of growth process which can be found among various taxonomic classes such as sponges and  Read more...

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Document Type: Book
All Authors / Contributors: Jaap A Kaandorp; Przemyslaw Prusinkiewicz
ISBN: 0387566856 9780387566856 3540566856 9783540566854
OCLC Number: 797451587
Description: XIII, 208 p. : ill. ; 29 cm
Contents: 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.- 2.6.1 Geometric Production Rules in 2D Modelling.- 2.6.2 The Geometric Modelling System for 2D Objects.- 2.6.3 Modelling a Growth Process in 2D with 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.- 3.6.1 The Basic Construction: the generator.- 3.6.2 Modelling the Coherence of the Skeleton.- 3.6.3 Introduction of the Smallest Skeleton Element in the Model.- 3.6.4 Modelling the "Widening Effect".- 3.6.5 Formation of New Growth Axes.- 3.6.6 Disturbance of the Growth Process, Formation of Plates.- 3.6.7 Additional Rules for the Formation of Branches and Plates.- 3.6.8 Formation of Branches.- 3.6.9 A Combination of the Previous Models.- 3.7 A Model of the Physical Environment.- 3.7.1 The Light Model.- 3.7.2 A Combination of the Geometric Model and the Concentration Gradient Model.- 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.- 4.1.1 A Comparison of a Range of Actual Forms and the Virtual Objects.- 4.1.2 A Comparison of the Growth Forms of Haliclona oculata Collected in Different Localities.- 4.1.3 Determination of the Fractal Dimensions in a Range of Forms.- 4.2 An Experimental Verification of the Model.- 4.2.1 The Simulation Experiments.- 4.2.2 The Transplantation Experiments.- 4.2.3 Comparison of Growth Forms of the Transplants and Simulation Experiments.- 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.- 5.5.1 The Lattice Model.- 5.5.2 The Virtual Lattice, a Subdivision of Space.- 5.6 An Iterative Geometric Construction Simulating the Radiate Accretive Growth Process of a Branching Organism.- 5.6.1 The Initiator.- 5.6.2 The Basic Construction: the Generator.- 5.6.3 Isotropic Growth and the Insertion of New Elements.- 5.6.4 Anisotropic Growth and the Insertion of New Elements.- 5.6.5 Formation of Branches.- 5.6.6 The Coherence Conserving Rules.- 5.6.7 More Evolved Branching Objects and Collision Detection.- 5.6.8 A Model of the Influence of Light Intensity on the Growth Process.- 5.6.9 A Model of the Influence of Nutrient Distribution on the Growth Process.- 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.
Responsibility: Jaap A. Kaandorp ; foreword by P. Prusinkiewicz.

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