Science in general, and ecology in particular, often proceed from the identification of patterns or propensities to the construction of theories, then back to the detailed analysis of the patterns, toward the development of more powerful theories (Peters 1992; Levin 1993), or the quantification of the propensities (Popper 1996). Thus, pattern recognition and explanation of the related propensit...

This paper analyses, on an individual plant basis, the various components determining seed production in the evergreen shrub Lavandula latifolia (Labiatae), in order to estimate their relative contributions to individual differences in fecundity. The relationships between fecundity and age, size, and growth rate are also examined. Experimental pollination and watering were done in an attempt to...

Wondering about a childhood doodle compels us to ask a series of questions, which will lead us on a tour of increasingly sophisticated ideas from many parts of mathematics. Let me tell you about a doodle I did when I was very small, and the mathematics that flows inevitably from it. It looks like play, but in my mind this is what mathematics is really about: finding patterns in nature, explaini...

Cleistogamy is more common in grasses than in any other angiosperm family. Both self-fertilized cleistogamous (CL) spikelets and open-pollinated chasmogamous (CH) spikelets are typically produced. Relative allocation to CL and CH varies among species and populations, and is influenced by ontogeny and environment. The balance between reproductive modes can be expressed as a CH/CL ratio. This rat...

We consider classes of sets of r-adic expansions of reals speciied by means of the theory of formal languages or automata theory. It is shown how these speciications are used to calculate the Hausdorr dimension and Hausdorr measure of such sets. Since the appearence of Mandelbrot's 11 book \Fractals, Form, Chance and Dimen-sion" Fractal Geometry as a means providing a theory describing many of ...

The Cross-Newell phase diffusion equation, τ(|E k|)2T = −∇ · (B(|E k|) · E k), E k = ∇2, and its regularization describes natural patterns and defects far from onset in large aspect ratio systems with rotational symmetry. In this paper we construct explicit solutions of the unregularized equation and suggest candidates for its weak solutions. We confirm these ideas by examining a fourth-order r...

In 1952, Alan Turing, a British mathematician best known for his work on code-breaking and artificial intelligence, was convicted of engaging in homosexual acts and sentenced to chemical castration. Amid that personal drama, he still found the time to publish a visionary paper on the mathematics of regularly repeating patterns in nature, which could be applied to the stripes on tigers and zebra...