Scott Hotton

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Morphogenesis of plant cells is tantamount to the shaping of the stiff cell wall that surrounds them. To this end, these cells integrate two concomitant processes: 1), deposition of new material into the existing wall, and 2), mechanical deformation of this material by the turgor pressure. However, due to uncertainty regarding the mechanisms that coordinate(More)
We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the(More)
This article presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems. We introduce the concept of ontogenetic graph as a parsimonious and mechanistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the(More)
The filaree (Erodium cicutarium), a small, flowering plant related to geraniums, possesses a unique seed dispersal mechanism: the plant can fling its seeds up to half a meter away; and the seeds can bury themselves by drilling into the ground, twisting and untwisting in response to changes in humidity. These feats are accomplished using awns, helical(More)
The calculation of divergence angles between primordia in a plant apex depends on the point used as the center of the apex. In mathematically ideal phyllotactic patterns, the center is well defined but there has not been a precise definition for the center of naturally occurring phyllotactic patterns. A few techniques have been proposed for estimating the(More)
We define a mathematical formalism based on the concept of an ‘‘open dynamical system’’ and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes(More)
Historically cognition was understood as the result of processes occurring solely in the brain. Recently, however, cognitive scientists and philosophers studying “embodied” or “situated” cognition have begun emphasizing the role of the body and environment in which brains are situated, i.e. they view the brain as an “open system”. However, these theorists(More)
Cell differentiation often appears to be a stochastic process particularly in the hemopoietic system. One of the earliest stochastic models for the growth of stem cell populations was proposed by Till et al. in 1964. In this model there are just two cell types: stem cells and specialized cells. At each time step there is a fixed probability that a stem cell(More)
In recent years computer models have become increasingly important in providing insights into the developmental process of plants. The study of phyllotactic patterns provides a good example of this. Despite the huge diversity of plant forms there are only a few ways in which plant organs such as leaves, florets, scales, etc. are arranged along a plant stem.(More)