Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

Symmetries [in biological systems]

Biological systems often show definite discrete symmetry. (In monocotyledon plants there is usually 3-fold symmetry; in dicotyledons 4- or 5-fold. Animals like starfish often have 5-fold symmetry; higher animals usually only 2-fold symmetry. There are fossils with 7- and 9-fold symmetry. At microscopic levels there are sometimes other symmetries: cilia of eukaryotic cells can for example show 9- and 13-fold symmetry. In the phyllotaxis process discussed in the main text one new element is produced at a time. But if several elements are produced together the same basic mechanism will tend to make these elements be equally spaced in angle—leading to overall discrete symmetry. (Individual proteins sometimes also arrange themselves into overall structures that have discrete symmetries—which can then be reflected in shapes of cells or larger objects.) (See also page 1011.)

From Stephen Wolfram: A New Kind of Science [citation]