Plants gray-green or bluish green, rarely green, homophyllous or subheterophyllous. Stems 1-3, erect to ascending, ± unbranched, 5-15 cm, or numerous, procum-bent, mat-forming, extensively branched, 20-70(-200) cm. Leaves: ocrea 3.5-6.5(-8) mm, proximal part cylindric, distal part silvery, relatively persistent, with inconspicuous veins, leaving almost no fibrous remains after disintegrating; petiole 0.3-2(-3.5) mm; blade green or gray-green, lateral veins visible but not raised abaxially, lanceolate to elliptic, oblanceolate, or obovate, 6-30(-45) × 3-6(-13) mm, 2.5-5.6(-10) times as long as wide, apex acute to obtuse; stem leaves 1-2.5 times as long as branch leaves. Cymes mostly uniformly distributed, but also aggregated at tips of stems and branches, 2-6-flowered. Pedicels mostly enclosed in ocreae, 1-2.5 mm. Flowers: perianth (2-)2.3-3.4(-3.6) mm, 0.9-1.3(-1.5) times as long as wide; tube 20-36% of perianth length; tepals overlapping, green with white or sometimes pink margins, oblong, apex cucullate, outer tepals pouched at base; veins branched, moderately to strongly thickened; stamens 7-8. Achenes usually enclosed in perianth, light brown to brown, ovate, 3-gonous, (1.8-)2-2.8(-3) mm, faces subequal, concave to flat, apex straight, coarsely striate-tubercled to obscurely tubercled; late-season achenes common, 2.5-5 mm. 2n = 60. Flowering Jul-Nov. Roadsides, vacant lots, sidewalks, packed and nondrifting sands, borders of marshes and dunes; 0-3500 m; Alta., B.C., Man., N.B., Nfld. and Labr., N.W.T., N.S., Ont., Que., Sask., Yukon; Ala., Alaska, Ariz., Ark., Calif., Colo., Conn., Del., D.C., Idaho, Ill., Ind., Iowa, Kans., Ky., La., Maine, Mich., Minn., Miss., Mo., Mont., Nebr., Nev., N.H., N.J., N.Mex., N.Y., N.C., N.Dak., Ohio, Okla., Oreg., Pa., R.I., S.C., S.Dak., Tenn., Tex., Utah, Vt., Va., Wash., W.Va., Wis., Wyo. Although apparently it has a North American origin, subsp. buxiforme is considered part of the Polygonum aviculare complex because it intergrades with subsp. aviculare (M. Costea and F. J. Tardif 2003).
From Flora of Indiana (1940) by Charles C. Deam
This species is very local but I believe when the knotweeds are studied more intensively it will be found throughout the state.
Indiana Coefficient of Conservatism: C = null, non-native
Prostrate, freely branched and mat-forming, homophyllous annual; lvs oblong to oblanceolate, 3-20 נ1-8 mm; ocreae to 5 mm, hyaline-silvery distally; pedicels barely exsert; mature perianth 2-3 mm, divided to below the middle, the undivided part asymmetric, ventricose on one side, the segments greenish with white or pinkish margins; outer 3 segments cucullate; achenes 2-2.8 mm, included, dark brown, minutely striate-papillose, one side broader; late-season frs exsert, to 4.5 mm, olivaceous, smooth; 2n=60. Packed, nondrifting sands, borders of marshes and dunes, and sandy soils, both maritime and inland; rare but widespread in the U.S. and s. Can.
Gleason, Henry A. & Cronquist, Arthur J. 1991. Manual of vascular plants of northeastern United States and adjacent Canada. lxxv + 910 pp.