Unformatted text preview: n rotational symmetries in the plane together with the n reﬂection symmetries form a group that is isomorphic to D n . See Exercise 2.3.10 . Figure 2.3.3 (below) has D 9 symmetry, while Figure 2.3.4 possesses Z 5 symmetry, but not D 5 symmetry. Both of these ﬁgures were gener-ated by several million iterations of a discrete dynamical system exhibit-ing “chaotic” behavior; the ﬁgures are shaded according to the probability of the moving “particle” entering a region of the diagram — the darker regions are visited more frequently. A beautiful book by M. Field and M. Golubitsky, Symmetry in Chaos (Oxford University Press, 1992), discusses symmetric ﬁgures arising from chaotic dynamical systems and displays many extraordinary ﬁgures produced by such systems....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08