Gaussian Schmidt Arrangement

The Gaussian Schmidt arrangement is the orbit of the extended real line and the hyperbolic geodesic plane it bounds in the upper half space model, under Mobius transformations of determinant 1 with Gaussian integer entries.  As such, it is a sort of illustration of the Picard Bianchi group.  This model shows only the circles (and their geodesic planes, i.e. hemispheres) inside the circle with diameter joining 0 and i.  Only circles up to curvature 18 are shown.  The largest geodesic hemisphere is chopped to show the Apollonian circle packing within, viewed from infinity.  For more, see math.katestange.net.