[edit] In nature
The 53rd plate from
Ernst Haeckel's
Kunstformen der Natur (1904), depicting organisms classified as
Prosobranchia (now known to be polyphyletic).
The study of spirals in
nature have a long history,
Christopher Wren observed that many
shells form a
logarithmic spiral.
Jan Swammerdam observed the common mathematical characteristics of a wide range of shells from
Helix to
Spirula and
Henry Nottidge Moseley described the mathematics of
univalve shells.
D’Arcy Wentworth Thompson's
On Growth and Form gives extensive treatment to these spirals. He describes how shells are formed by rotating a closed curve around a fixed axis, the
shape of the curve remains fixed but its size grows in a
geometric progression. In some shell such as
Nautilus and
ammonites the generating curve revolves in a plane perpendicular to the axis and the shell will form a planar discoid shape. In others it follows a skew path forming a
helico-spiral pattern.
Thompson also studied spirals occurring in
horns,
teeth,
claws and
plants.
[1]
Spirals in plants and animals are frequently described as
whorls.
A model for the pattern of
florets in the head of a
sunflower was proposed by H Vogel. This has the form
where
n is the index number of the floret and
c is a constant scaling factor, and is a form of
Fermat's spiral. The angle 137.5° is related to the
golden ratio and gives a close packing of florets.
[2]
[edit] In art
The spiral has inspired artists down the ages. The most famous piece of 60s Land Art was Robert Smithson's Spiral Jetty, at the Great Salt Lake in Colorado. The theme continues in David Wood's Spiral Resonance Field at the Balloon Museum in Albuquerque.
[edit] References
- <LI id=cite_note-0>^ Thompson, D'Arcy (1917,1942), On Growth and Form
- ^ Prusinkiewicz, Przemyslaw; Lindenmayer, Aristid (1990). The Algorithmic Beauty of Plants. Springer-Verlag. pp. 101–107. ISBN 978-0387972978. http://algorithmicbotany.org/papers/#webdocs.
[edit] See also