A comprehensive model for acrotonic, mesotonic and basitonic branchings in plants

Lück, Jacqueline; Lück, Hermann B.; Bakkali, Mohammed

doi:10.1007/bf00047243

Cited by 11 publications

(8 citation statements)

References 7 publications

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“…Frijters and Lindenmayer observed [25] that simple control of development by lineage, expressed by non-parametric context-free L-systems, could not capture basipetal flowering sequences (with the flowering zone progressing from the top of the plant downwards) and acrotonic patterns of branch development (with the largest branches situated near the top of the plant). A formal analysis supporting this observation was presented later by Lück et al [67] and Prusinkiewicz and Kari [93]. Overcoming this limitation, Janssen and Lindenmayer [50]and Lindenmayer showed [62] that acrotonic flowering patterns and basipetal flowering sequences could be reproduced assuming control of development by hormones that flow through the developing structure and trigger developmental events.…”

Section: Applications To Plant Modelingmentioning

confidence: 81%

A look at the visual modeling of plants using L-systems

Prusinkiewicz

1999

Agronomie

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This paper presents a retrospective look at the history of plant modeling using L-systems, and a guide to the literature in the field. The topics include: distinctive features of the original L-system formalism, its subsequent extensions, visualization of L-system models, modeling of interactions between plants and their environment, the use of Lsystems as a plant modeling language, and a survey of applications. (© Inra/Elsevier, Paris.) L-system / plant development / simulation model Résumé-Un aperçu de la modélisation visuelle des plantes à l'aide des L-systèmes. Cet article présente une rétrospective de la modélisation des plantes à l'aide des L-systèmes ainsi qu'un guide bibliographique pour ce domaine. Les sujets traités comprennent : les caractéristiques distinctives du formalisme du L-système original, ses développements ultérieures, la modélisation des interactions entre les plantes et leur environnement, l'utilisation des L-systèmes comme langage pour modéliser les plantes et une vue d'ensemble des applications. (© Inra/Elsevier, Paris.) L-système / développement / plante / modèle de simulation Communicated by Gérard Guyot (Avignon, France)

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Section: Applications To Plant Modelingmentioning

confidence: 81%

A look at the visual modeling of plants using L-systems

Prusinkiewicz

1999

Agronomie

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“…5,30 Consequently, several more powerful mechanisms have been proposed in the literature. Specifically, Lück et al 17 described a model in which the meristems can count. As shown in Figure 13, the apex of the main axis counts the segments that it has created so far, and assigns the resulting values to the counters associated with the newly created lateral apices.…”

Section: Multiple Blind Agents With Infinite Memorymentioning

confidence: 99%

Paradigms of Pattern Formation: Towards a Computational Theory of Morphogenesis

Prusinkiewicz¹

2000

Pattern Formation in Biology, Vision and Dynamics

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The variety of natural patterns makes it difficult to analyze and compare them in a systematic manner. We address this problem by focusing on the computational aspects of pattern formation processes. They are characterized in terms of the number of morphogenetic agents, the computing capability of each agent, and the forms of information transfer between the agents and their environment. This computational analysis can be applied to a wide range of patterns. It highlights the fundamental, algorithmic similarities between processes that may be implemented using different physical or physiological mechanisms in nature. It also confirms earlier observations that similar or identical patterns can be created by fundamentally different processes. The tradeoffs between computational characteristics of these processes lend themselves to a formal analysis, which could lead to the formulation of a "computational theory of morphogenesis" on the basis of the theory of algorithms. ReferencePrzemyslaw Prusinkiewicz: Paradigms of pattern formation: Towards a computational theory of morphogenesis. In Pattern Formation in Biology, Vision, and Dynamics, pp. 91−95. PARADIGMS OF PATTERN FORMATION: TOWARDS A COMPUTATIONAL THEORY OF MORPHOGENESISPRZEMYSLAW PRUSINKIEWICZ Department of Computer Science, The University of Calgary 2500 University Dr. N.W., Calgary, Alberta T2N 1N4, Canada E-mail: pwp@cpsc.ucalgary.caThe variety of natural patterns makes it difficult to analyze and compare them in a systematic manner. We address this problem by focusing on the computational aspects of pattern formation processes. They are characterized in terms of the number of morphogenetic agents, the computing capability of each agent, and the forms of information transfer between the agents and their environment. This computational analysis can be applied to a wide range of patterns. It highlights the fundamental, algorithmic similarities between processes that may be implemented using different physical or physiological mechanisms in nature. It also confirms earlier observations that similar or identical patterns can be created by fundamentally different processes. The tradeoffs between computational characteristics of these processes lend themselves to a formal analysis, which could lead to the formulation of a "computational theory of morphogenesis" on the basis of the theory of algorithms.

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“…Les systbmes h r66criture parall~le de type L (Lindenmayer, 1968), les algorithmes g6om6triques (Honda, 1971) ou d'autres formulations (Eyrolles, 1986) et, plus r6cemment, le systbme d'6quations lin6aires appliqu6 ~t chaque r66criture (LOck et LOck, 1988et 1990 utilisent des r~gles de production qui contiennent, pour un arbre donn6, l'ensemble de sa structure topologique. Liaison entre construction th6orique et m6moire num6rique du d6veloppement La mod61isation de la croissance des arbres botaniques a &6 entreprise essentiellement h partir de syst~mes de d6veloppementexprim6s sous une forme algorithmique.…”

Section: Repr6sentation Graphique De La M6moire Num6riqueunclassified

Infogenese en biologie vegetale

Hunault

Beaujard²,

Lück

et al. 1991

Acta Biotheor

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The construction of theoretical models in biology, situated at the cross-roads of biology, mathematics and computer science, otten leads to a tool as final product. Its genesis can be named 'Infogenesis'. The procedure of the resolution of theoretical problems is analyzed on examples of practical purposes taken from plant biology.The first example deals with mineral plant nutrition, explaining a way to go from theoretical ionic balances to the experimental realization of nutritional solutions with macro-element components.The balanced concentrations of ions are expressed in terms of concentrations of electrical charges (milli-equivalent per litre). The neutral combination of anions and cations results from salts, acids or bases introduced in water. To achieve this combination, a table lines up concentrations in cations in the last column and concentrations of anions in the bottom line, their sums being equal. The obtained quantities of salts appear at the intersections of lines and columns. An expected ionic equilibrium is equivalent to the filling up of the table considered as a mathematical matrix. The algorithm constructing the table permits e.g. to use fewer salts or some salts preferentially. The procedure minimizing the values of elements corresponding to non-desired salts is presented. A prior order, which is the reverse to the use of preferential anion/cation pairs, is required for the successive treatments of the elements.An algorithm of "successive splittings" respects the weights of sums in lines and columns. It mainly looks for the maximal quantity that can be taken from a chosen box in the table i.e. from the salts, and carries out its splitting. The repetition of this operation takes into account the impossibility to add a positive value to a minimized term. Therefore, during the operation, some lines and columns have to be "frozen", i.e. their values are considered as unchangeable. The number of rewritings of the table by the splitting method depends on the order of treatment of the elements, their number and the weight of lines and columns.The method gives a global approach of the mineral nutrition in terms of ion concentrations. An initial chemical definition of the problem leads to the constructions of algorithm on the basis of the successive splitting method. It is resolved mathematically and computerized via a dynamic arrangement of elements in the table. The determination of salts formulas from the known ionic concentrations is the practical objective and the filling up of the table is the computerized means. Initial data is the sums in lines and columns. The resolution is accomplished by the weighted redistribution of the values taken from each box in the table. The realization is done within a loop of calculations, rewriting the terms of the grid according to a predefined preferential order.In a second example, a procedure opening the way to the construction of the form for a plant from empirical data is discussed. The study of the vegetative development of woody ornamental plants is necess...

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A comprehensive model for acrotonic, mesotonic and basitonic branchings in plants

Cited by 11 publications

References 7 publications

A look at the visual modeling of plants using L-systems

A look at the visual modeling of plants using L-systems

Paradigms of Pattern Formation: Towards a Computational Theory of Morphogenesis

Infogenese en biologie vegetale

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