[tcjryoiw] Octagonal grid

First, two perpendicular lines in a plane.  4 unit circles tangent to both lines.  Four 45-degree rays from the origin to infinity, except omitting the portion between the origin and the center with the circle.  Repeat, inserting more unit circles between adjacent rays, then shooting a new ray out from each circle.

This accomplishes a radial pattern with approximately constant density of lines per area.  Street layout. Spiderweb.

Draw equally spaced concentric circles around the origin and mark where they intersect the rays.  This accomplishes an approximately constant density of radially symmetric points.

What pattern do the centers of the unit circles form?  The tangent points might also be interesting.