MLA 31500

Natural Sciences Elective

 

Order and Chaos in the Natural World

 

Spring Quarter 2008

 

Links to Useful and Interesting Web Sites

March 20, 2008

 

All of the links listed below appear to reach useful sources of information regarding order and chaos in the natural world.  There are many more web sites than can be listed here.  Therefore, users are urged to exploit the links at the sites listed here and to search the web independently for other interesting sites.  I might update this page occasionally during the Spring Quarter.  Any student who finds a particularly good site not listed here is invited to send me the URL via e-mail at voort@oddjob.uchicago.edu.

 

TWO GENERAL SITES

 

1.         Wolfram Research's web site World of Science, A Wolfram Web Resource at http://scienceworld.wolfram.com/ covers many fields of mathematics, physics, and chemistry.  Entries range from definitions of only a few lines to extended (often mathematical!) essays.  In order to reach many entries relevant to order and chaos, click on ÒPhysics,Ó then on ÒMechanics,Ó and finally on a suitable key word.  Biographical information on workers in many fields of science is also found at this site.

 

2.         The Archives of Mathematics has a home page at http://archives.math.utk.edu/ a page that links to many other resources.  Of particular use is the page Topics in Mathematics at http://archives.math.utk.edu/topics/.  The topics ÒDynamical Systems,Ó ÒFractals,Ó and ÒNonlinear DynamicsÓ list particularly useful links for our purposes.

 

INTRODUCTIONS TO CHAOS

 

3.         A rather better introduction with some illuminating animations is to be found at the web site http://johnbanks.maths.latrobe.edu.au/chaos/ which presents Chaos: A pictorial introduction by a mathematics group at La Trobe University.

 

4.         An even more comprehensive  but still brief introduction to the subject is contained in THE CHAOS HYPERTEXT BOOK by Glenn Elert at http://hypertextbook.com/chaos/.  The illustrations are quite good at this site.

 

CELESTIAL MECHANICS

 

5.         Jack Wisdom gives A Brief Introduction to Chaos in the Solar System at http://geosys.mit.edu/~solar/text/short.html or http://geosys.mit.edu/~solar/notes/notes.html.  At the time of this revision, I have been unable to reach these sites.  However, I have left them on the list because the problem might be only temporary, and Wisdom is one of the great masters of chaos in dynamical astronomy.

 

THE ANTIKYTHERA MECHANISM

 

6.         Rupert Russell has put a collection of material on the Antikythera Mechanism on a web site at http://www.giant.net.au/users/rupert/kythera/kythera.htm.  This site includes links to a number of other relevant sites and, in particular, links to a Scientific American article by Derek J. de Solla Price.

 

7.         With adequate computing power, one could look at the simulations and other images of the Antikythera Mechanism at http://etl.uom.gr/mr/Antikythera/index.html.

 

THE DOUBLE PENDULUM

 

8.         A technical analysis of the double pendulum can be found at the site http://scienceworld.wolfram.com/physics/DoublePendulum.html,  Near the bottom of this page, there is an animation of the chaotic motion of a double pendulum.

 

9.         M. Kawaka has put a two simulations of a double pendulum at the web page at http://www6.ocn.ne.jp/~simuphys/niju-furikoE.html.

 

CHAOS AND FRACTALS

 

              Here is a short list of sites worth visiting.

 

10.      Thinkquest, Chaos & Fractals at http://library.thinkquest.org/3703/frame.html?tqskip1=1&tqtime=0407.  This is a good source for attractors and fractals.  Text, programs, and illustrations are all useful.

 

11.      Zoom on the Mandelbrot Set at http://www.lut.ac.uk/departments/ma/gallery/mandel/index.html.

 

12.      The Fractal Geometry of the Mandelbrot Set at http://math.bu.edu/DYSYS/FRACGEOM/index.html and at http://math.bu.edu/DYSYS/FRACGEOM2/FRACGEOM2.html.

 

13.      Rupert RussellÕs web page at http://www.giant.net.au/users/rupert/ includes a section on fractals.

 

14.      Julia and Mandelbrot Set Explorer at http://aleph0.clarku.edu/~djoyce/julia/explorer.html.

 

SMALL BODIES IN THE SOLAR SYSTEM AND TERRESTRIAL IMPACTS

 

15.      There is a substantial geological record of impacts of small bodies (asteroids and/or comets) with Earth.  The University of New Brunswick runs a database with relevant links at http://www.unb.ca/passc/ImpactDatabase/.

 

16.      Candidates for the impacting bodies are the Near Earth Objects (NEOs).  The NASA Nearth Earth Object Program is described at http://neo.jpl.nasa.gov/.

 

17.      The Harvard-Smithsonian Center for Astrophysics operates the NEO Page at http://cfa-www.harvard.edu/iau/NEO/TheNEOPage.html.

 

18.      Many years ago, Gerard P. Kuiper postulated that a belt of comets beyond the orbit of Neptune would be a source of comets in the inner solar systems.  ÒKuiper Belt ObjectsÓ are now observed in substantial numbers.  Resonances with the orbit of Neptune and the chaotic behavior that can result make the dynamics of KBOs a subject of great interest.  David Jewitt, one of the early discoverers of KBOs has an authoritative web site at http://www.ifa.hawaii.edu/faculty/jewitt/kb.html.

 

THE LORENZ WATER WHEEL

 

19.      When we Goggle ÒLorenz Water Wheel,Ó we find many web sites.  Here is a site with an instructive simulation: http://education.mit.edu/starlogo/models/library/LorenzWaterWheel.

 

20.      And here is a site describing a physical model and a movie of the model in operation: http://www.uea.ac.uk/~f029/waterwheel.html.  You have to look carefully at the end of the page in order to find the link to the movie.  This is the Lorenz attractor in operation.

 

LINKS:

 

Return to Course Page: mla315spring2008.htm

 

Return to Peter Vandervoort's Home Page: pov.html

 

Go to the home page of the Department of Astronomy and Astrophysics

of the University of Chicago:  http://astro.uchicago.edu/