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The Mathematics and Computer Graphics of Spirals in Plants

This is a study of the pattern known as spiral phyllotaxis—literally, “leaf-arrangement”, but applied to the arrangement of seeds, florets, petals, scales, twigs and so on—and which is very widespread in plants. A number of stages in the refinement of model-making are recorded. In particular, the model illustrated in the literature on the subject indicating uniform growth is taken a step further in generality to indicate non-uniform growth.  The intention has been to arrive at a wholly visual statement. And yet the mathematical approach is integral to this end. The study of flower forms becomes a study of the relation between the circle and the golden ratio.  A computerised drawing system was used to draw forms that are algebraically defined. This solved a technical problem, but also gave me a glimpse of the enormous scope opened up by this electronic tool. To draw, for example, a simple equi-angular spiral (as found in snail shells) is difficult and time-consuming by traditional means, but elementary by computer.