Recursion: Real and Imaginary Inflorescences (UMAP)

When a colleague from the Biology Dept. who knew I was interested in flowers introduced me to C.L. Porter's Taxonomy of Flowering Plants [1967], I was struck immediately by the diagrams of the common inflorescences. An inflorescence is the arrangement of flowers on a plant. The diagrams in Porter's book are simple stick figures with small disks representing the individual flowers. At the time, I was teaching a course in computer graphics and was on the lookout for examples of recursion and examples that illustrate the utility of simple geometry and trigonometry. Here was a great source! I have always been fascinated with recursion and the nature-like forms that it produces, and I feel that it is a neglected topic in teaching mathematics and computer science. In biology, we learn that the tiny seed of a real plant contains all of the information necessary to ensure that the plant looks like other plants of its species. In an analogous manner, a simple recursive process generates a family of computer-graphical "plants." The first word out of one of my students when she saw her creation growing on the screen was "Awesome!" In this Minimodule, I first indicate how to generate diagrams of some of the common inflorescences described in Porter's book, using simple recursive functions. Then we allow our imagination to take over and combine two or more of the functions to produce purely imaginary inflorescences.

Table of Contents:

INTRODUCTION

COMMON INFLORESCENCES

DEFINING A RECURSIVE PROCEDURE

IMAGINARY INFLORESCENCES

CONCLUSION

REFERENCES

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