I am considering a problem that is asking me to explore a deceptively simple dynamical system and discover some of surprising properties. I want to consider the motion of four particles A,B,C and D in the plane. The particles start at four random points in the plane. Each particle moves with unit speed. A moves towards B, B towards C, C towards D and D towards A. What happens (qualitatively), and how (quantitatively, in terms of, say, angles and log distances)? I was wondering if somebody could give me some direction in terms of the the simplest case, when the starting positions form a square.
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1http://www.mathworks.com/matlabcentral/newsreader/view_thread/18462?requestedDomain=www.mathworks.com – vadim123 Apr 13 '16 at 18:39
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1http://www.mrlsmath.com/geogebra/geogebra-materials/spiraling-squares-ants-problem/ – vadim123 Apr 13 '16 at 18:39
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Please avoid the tags [tag:undergraduate-research] and [tag:research]. We are trying to remove them. – Caleb Stanford Jul 24 '16 at 19:41