Development, Growth and Time

Vitányi, Paul M. B.

doi:10.1007/978-3-642-95486-3_37

Cited by 4 publications

(1 citation statement)

References 6 publications

(13 reference statements)

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“…In practice it is often difficult, if not impossible, to find L-systems Limitations with the required growth functions. Vitányi [153] illustrates this by referring to sigmoidal curves:…”

Section: Growth Functionsmentioning

confidence: 99%

The Algorithmic Beauty of Plants

Prusinkiewicz

Lindenmayer²

1990

The Virtual Laboratory

1,930

1,232

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With 150 Illustrations, 48 in ColorThis edition of The Alogirthmic Beauty of Plants is the electronic version of the book that was published by Springer-Verlag, New York, in 1990 and reprinted in 1996. The electronic version has been produced using the original L A T E X files and digital illustrations. Front cover design: The roses in the foreground (Roses by D. R. Fowler, J. Hanan and P. ) were modeled using L-systems. Distributed ray-tracing with one extended light source was used to simulate depth of field. The roses were placed on a background image (photgraphy by G. Rossbach), which was scanned digitally and post-processed. PrefaceThe beauty of plants has attracted the attention of mathematicians for Mathematics and beauty centuries. Conspicuous geometric features such as the bilateral symmetry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most extensively. This focus is reflected in a quotation from Weyl [159, page 3], "Beauty is bound up with symmetry."This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, characterized by Mandelbrot [95, page 34] as follows:When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar.This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg [61]:In many growth processes of living organisms, especially of plants, regularly repeated appearances of certain multicellular structures are readily noticeable.... In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage.Thus, self-similarity in plants is a result of developmental processes.Growth and form By emphasizing the relationship between growth and form, this book follows a long tradition in biology. D'Arcy Thompson [143] traces its origins to the late seventeenth century, and comments:Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space. This concept is echoed by Hallé, Oldeman and Tomlinson [58]:The idea of the form implicitly contains also the history of such a form. vi PrefaceThe developmental processes are captured using the formalism of L-systems. They were introduced in 1968 by Lindenmayer [82] as a Modeling of plants theoretical framework for studying the development of simple multicellular organisms, and subsequently applied to investigate higher plants and plant organs. After the incorporation of geometric features, plant models expressed using L-systems became detailed enough to allow the use of computer graphics for realistic visualization of p...

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“…In practice it is often difficult, if not impossible, to find L-systems Limitations with the required growth functions. Vitányi [153] illustrates this by referring to sigmoidal curves:…”

Section: Growth Functionsmentioning

confidence: 99%

The Algorithmic Beauty of Plants

Prusinkiewicz

Lindenmayer²

1990

The Virtual Laboratory

1,930

1,232

View full text Add to dashboard Cite

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Applications of L-systems to computer imagery

Prusinkiewicz

1987

Lecture Notes in Computer Science

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Sur la notion de limite interne et externe dans les fonctions de croissance monotones. Une reformulation de l'équation logistique

Buis

Lück²

2006

Comptes Rendus. Biologies

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La valeur limite (« à saturation ») des fonctions de croissance non périodiques constitue l'un des paramètres de divers modèles usuels, comme l'équation logistique. Son interprétation est double, représentant, soit une limite de nature interne ou endogène, soit une limite externe dépendant de l'environnement. Reprenant notre modèle autocatalytique de populations cellulaires structurées (Buis, modèle II, 2003), nous proposons une reformulation de l'équation logistique, illustrée dans le cas de trois classes de cellules (juvéniles, matures, sénescentes). La composante agoniste correspond exactement à la seule fraction active de la population (cellules matures non sénescentes), alors que la composante antagoniste s'interprète comme une limite externe (source ou substrat disponible). L'existence et les modalités d'une limite interne sont étudiées sur la base de ce même modèle de type autocatalytique, avec deux modification essentielles : absence de compétition (source non limitante), existence d'un nombre maximal de mitoses par lignée cellulaire (Lück et Lück, 1978). L'analyse, conduite selon le principe des automates cellulaires déterministes (L-systèmes), montre la flexibilité de ce modèle, qui exhibe une diversité de propriétés cinétiques : écarts à la forme sigmoïde, nombre et position des extremums de la vitesse de croissance, nombre de phases de la structure temporelle. Ceci correspond bien à la diversité des courbes expérimentales de croissance, dont les singularités du gradient de la vitesse de croissance ne peuvent souvent être correctement expliquées par les modèles globaux usuels.

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Development, Growth and Time

Cited by 4 publications

References 6 publications

The Algorithmic Beauty of Plants

The Algorithmic Beauty of Plants

Applications of L-systems to computer imagery

Sur la notion de limite interne et externe dans les fonctions de croissance monotones. Une reformulation de l'équation logistique

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