quantum_chaos_250.08.gif For SL(2,Z), R about 250.

quantum_chaos_500_cor.gif In a non-arithmetic group, R about 500.

quantum_chaos_250.07_cor.gif Likewise, but R about 250.

map.02.gif The trajectory of a closed horocycle with very small y-value on the modular domain SL(2,Z)\H.

map.04.gif Another such, but in a non-arithmetic group.

uppsala.1.gif A Maass waveform (i.e., quantum-mechanical particle) for SL(2,Z)\H having eigenfrequency R about 6051. Light blue depicts regions with highest probability. Core data produced by DH on ``Riemann'', a Cray YMP-EL4/1024 at Uppsala University, in the mid-1990s. What do you see???

thesis_gaussian_clt5.218.gif Automorphic function value-statistics along a closed horocycle in a non-arithmetic group. Using Cray-T3D. (There appears to be a central limit theorem as y tends 0.)

thesis_non_gaussian_clt3.224.gif Automorphic function value-statistics along a closed horocycle in SL(2,Z). Using Cray-T3D. (No central limit theorem.)

plot.08d.gif Histogram of an automorphic form's value along some closed horocycles in a non-arithmetic triangle group.