Carpet tiles having patterns and color schemes that obviate the need to orient the tiles in a particular positional or rotational relationship relative to each other. The tiles exhibit orthogonal ambiguity, meaning that they may be laid in any side-by-side orientation with respect to adjacent tiles without looking out of place to the ordinary viewer and thereby still achieving an appearance of continuity like broadloom carpet. Each tile has patterns of shapes having some straight and curved elements. At least some of the straight elements on each tile preferably parallel a tile edge. The shapes are formed from a color or combination of colors so that adjacent shapes on each tile have at least one color in common. Furthermore, each tile has at least one color in common with every other tile, so that when the tiles are laid, the colors on adjacent tiles coordinate. Moreover, because the pattern on each tile appears random, placement of the tiles on the floor in any side-by-side orientation simply creates a larger, apparently random pattern, rendering it impossible for any tile to look out of place.