Wide-bandwidth H I 21 cm maps made with the Hat Creek 26 m (85 foot) telescope toward the Galactic anticenter reveal a wealth of filamentary structure at intermediate negative velocities. In order to study this filamentary structure, a median filtering technique is used to remove the smooth, large-scale background. Structures with widths less than about 5-degrees are preserved. The filaments are untangled from one another by following those that have continuous velocity gradients. The selected filaments are oriented parallel to the Galactic plane and cover a range of lengths between 7-degrees and 40-degrees. Their appearance is similar to lines of constant longitude on the surface of a tilted sphere centered near l = 185-degrees, b = 0-degrees with a radius of about 25-degrees. They are easily visible at intermediate velocities but become tangled in a web of filamentary structures at velocities greater than -17 km s-1 relative to the local standard of rest. I fit models of filaments on the surface of such a sphere to the data. The models are constrained to match the observations in both projected position and radial velocity. Velocity fields resulting from systemic motion, spherical expansion, differential rotation, and poloidal motion along the surface of the sphere from the poles toward the equator are considered. There is little, if any, evidence in the velocity fields for the filaments being on the surface of an expanding or contracting sphere. The spherical morphology may still be correct, but no robust signature of spherical expansion or poloidal motion resulting from a uniform magnetic field is observed. The overall negative radial velocities of the filaments (approximately 30 km s-1) are explained as arising either from the noncircular orbits of gas in the Galaxy or from the impact of high-velocity clouds, observed toward the anticenter, with the disk in the outer Galaxy. The feasibility of these explanations depends upon the distance to the high-velocity clouds and intermediate-velocity filaments. If they are within a few kiloparsecs of the Sun, then the impact origin is preferred. In this case, the filaments are remnants of a previous impact betweeen an Anticenter Chain high-velocity cloud and the disk. If they are more distant, then these clouds and filaments cover a vast extent, and a global origin related to large-scale Galactic structure is more appropriate. Such noncircular orbits are natural if the Galaxy possesses a nonaxisymmetric or barlike gravitational potential.