Chaos theory, initially started in the 19th century by the French mathematician Henri Poincare and later realized by Lorenz, Feigenbaum and others, describes a system that is non-random and deterministic. Such a system undergoes a transition in which a large propagation of error inhibits long-term prediction. One of the most important developments in chaos was Feigenbaums universality constant ( = 4.6692) or his development in routes to Chaos in periodic systems using the quadratic iterator xn+1= axn(1-xn), where n=0,1,2 etc which is graphically represented in Feigenbaum’s diagram. A magnetic compass needle when placed in the Earth’s magnetic field and subjected to a sinusoidally varying magnetic field can display chaotic behavior depending on the strength and frequency of the imposed magnetic field. Chaotic motion can be determined by measuring the speed of the needle at a fixed location and plotting this as a function of the phase of the driving field. It is also possible to simulate this motion on the computer and to generate graphs of the expected behavior if one knows the magnetic moment of the needle, its moment of inertia, and the damping constant. In this experiment, we determined these parameters and then used a computer to monitor the speed at a fixed angle and observed period doubling followed by chaotic behavior.

**Jon Drieling, ’00** White Bear Lake, MN

Majors: Physics and Mathematics

**Chad Eimers, ’00** Waukee, IA

Majors: Physics and Mathematics

**James Levingston, ’00** Salem, MO

Majors: Physics and Geology

Sponsor: Harlan Graber