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(a) Construction of a Fibonacci spiral. The Fibonacci spiral is observed in sea shells of the species Argonauta argo (b) as well as in the growth of some species of ferns (c).

(a) Construction of a Fibonacci spiral. The Fibonacci spiral is observed in sea shells of the species Argonauta argo (b) as well as in the growth of some species of ferns (c).

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Modern methods of image analysis are based on the coordinates of the points making the silhouette of an image and allow the comparison between seed shape in different species and varieties. Nevertheless, these methods miss an important reference point because they do not take into consideration the similarity of seeds with geometrical figures. We p...

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... points dividing a golden rectangle into squares lie on a logarithmic spiral, which is sometimes known as the golden spiral [19,20] (Figure 5). The logarithmic spiral is a spiral whose polar equation is given by ...

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... Morphological variation in seed shape can be due to either genetic or environmental factors [38]. As the grapevine is normally propagated by vegetative propagation using stem cuttings, among the genetic factors, both the genetic composition of the parental cultivars in the initial crosses and those that were the male parents for the current generation may have an influence on the final phenotype [12]. ...
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... While seed shape usually remains relatively constant for each species, it can vary notably in some families. In certain plant families, like the Arecaceae and the Vitaceae [11,12], seeds resemble multiple types of geometric figures, while in others, a reduced number of morphological types are predominant, such as ellipses in the Campanulaceae [13] and Oleaceae [14], ovals in the Cucurbitaceae [15], Euphorbiaceae [16,17], and Rutaceae [13]. Seeds of the Caryophyllaceae present interesting features, with ovules hemianatropous to campylotropous [18][19][20], and the embryo corresponds to a peripheral type [21]. ...
... While seed shape usually remains relatively constant for each species, it can vary notably in some families. In certain plant families, like the Arecaceae and the Vitaceae [11,12], seeds resemble multiple types of geometric figures, while in others, a reduced number of morphological types are predominant, such as ellipses in the Campanulaceae [13] and Oleaceae [14], ovals in the Cucurbitaceae [15], Euphorbiaceae [16,17], and Rutaceae [13]. Seeds of the Caryophyllaceae present interesting features, with ovules hemianatropous to campylotropous [18][19][20], and the embryo corresponds to a peripheral type [21]. ...
... Seed shape quantification can be done by estimating the percentage surface shared between the seed image and a given model [13,25]. The resulting measurement has been termed the J index. ...
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Historically, little attention has been paid to the resemblance between seed silhouettes to geometric figures. Cardioid and derivatives, ellipses, heart curves, lemniscates, lenses, lunes, ovals, superellipses, waterdrops, and other figures can be used to describe seed shape, as well as models for quantification. Algebraic expressions representing the average silhouettes for a group of seeds are available, and their shape can be described and quantified by comparison with geometric models. Bidimensional closed-plane figures resulting from the representation of Fourier equations can be used as models for shape analysis. Elliptic Fourier Transform equations reproduce the seed silhouettes for any closed-plane curve corresponding to the contour of the image of a seed. We review the geometric properties of the silhouettes from seed images and discuss them in the context of seed development, plant taxonomy, and environmental adaptation. Silene is proposed as a model for the study of seed morphology. Three groups have been recently defined among Silene species based on the structure of their seed silhouettes, and their geometric properties are discussed. Using models based on Fourier Transform equations is useful in Silene species where the seeds are homogenous in shape but don’t adjust to described figures.