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According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

By the way, the circle is in general not a great circle. In fact, the process can be bidirectional, so there will be two accumulation point. The tangent points are like on a "tube in hyperbolic space" but not on a plane.

According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

By the way, the circle is in general not a great circle. In fact, the process can be bidirectional, so there will be two accumulation points. The tangent points are not on a plane but on a "tube in hyperbolic space" / "binodal cyclide" / "inversed circular cone" (help ... what's the standard name for this surface?) .

According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

By the way, the circle is in general not a great circle. In fact, the process can be bidirectional, so there will be two accumulation point. The tangent points are on a "binodal cyclide", not on a plane.

According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

By the way, the circle is in general not a great circle. In fact, the process can be bidirectional, so there will be two accumulation point. The tangent points are like on a "tube in hyperbolic space" but not on a plane.

According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

According to the discussion in Coxeter (1968), the tangent points lie asymptotically on a concho-spiral, so the distribution is not uniform on the sphere, but is uniform on a circle.

By the way, the circle is in general not a great circle. In fact, the process can be bidirectional, so there will be two accumulation point. The tangent points are on a "binodal cyclide", not on a plane.