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This applet demonstrates the generation of Glass patterns. The first click of "Graph" generates a random pattern of dots determined by "Number of Dots". Each subsequent click generates a linear transformation of the original pattern with a horizontal magnification "a", vertical magnication "b" and rotation angle "Theta". Example: Set "a=0.9", "b=1.1", and "Number of Dots"= 1000, "Theta=0" and hit "Graph" two times. Note the saddle (hyperbolic) geometry. Press "Clear" to reset. Now increase the value of "Theta" until you see a spiral geometry. Be sure to press "Clear" to reset before trying each different value of "Theta". See the Scholarpedia article on "Glass Patterns" for an explanation of the eigenvalues and how they reflect the geometry. |