The Mathematica Journal
Feature Articles
New Products
New Publications
News Bulletins
Write Us
About the Journal
Staff and Contributors
Back Issues
Download this Issue


There are many types of natural phenomena that can be represented by strings of characters. For example, the primary sequence of a protein is the order of amino acids that composes the macromolecular string. There are about twenty amino acids which are used as the building blocks of proteins. Each amino acid has a unique set of chemical and structural properties. Consequently, proteins can be conceptualized as finite words over a twenty-letter alphabet. The Fibonacci sequence is an infinite series that is derived from a model invented by Leonardo Pisano in the early thirteenth century to describe the population growth of rabbits. The series follows the recursive function . This sequence has been observed in many other systems and geometries found in nature. For example, it has been observed that many species of flowers have a total number of petals that is equal to a Fibonacci number. The proportions of many natural spirals such as those of pine cones, snail shells and nautilus shells also follow the Fibonacci sequence. Associated with this sequence is a binary -word generated by the morphism .

Mathematica can be used to perform many operations on strings. As a result, it can be used to produce unique demonstrations of the order inherent in certain strings. The focus of this project has been the development of graphic and musical demonstrations which reflect the order and symmetry inherent in strings found in nature.

Copyright © 2001 Wolfram Media, Inc. All rights reserved.

[Article Index][Next Page]