I lately got interested in heraldic design again (coats-of-arms and flags). Can we say anything interesting about hyperspatial design in the same style?
Other than a boring single solid color, the simplest device (I'll use that word to include both flags and shields) is a field divided in two colors by a single line or family of parallel lines. Obviously a 3-flat can be divided by planes. Heraldry avoids fussy distinctions, so there are just four common lines of division (— | \ /), with thirteen analogues in 3space: x=0, y=0, z=0, x=±y, y=±z, z=±x, x±y±z=0. Perpendicular lines, or planes, may be combined.
The line of division may be a wave, zigzag, square-wave and so on. A plane of division has a much richer range of such simple textures. Even a mere extrusion of a zigzag line has a degree of freedom, the direction of extrusion (though again this has only a few discrete values).
Next after partitions come the stripes (called ordinaries in heraldry): fess (horizontal), pale (vertical), bend (diagonal), bend sinister (the other diagonal), cross (pale+fess), saltire (diagonal cross). These have two sets of analogues: the thickened partition planes and their thickened normals; the latter may be thickened with a round or polygonal section (but I'm not sure this distinction is worth making in heraldry). Like a partition, an ordinary can have a pattern of bumps.
Another ordinary is the bordure, which follows the edge of the shield or flag. Its analogue may fully enclose the device, or only one (or more) of the partition planes.
Heraldry also makes abundant use of discrete figures called charges: stylized animals and plants, as well as stars, balls, rings, lozenges (diamonds) and whatnot. I won't discuss those now except to mention that they often occur in twos and threes, arranged along one of the partition lines or in triangle, two above one (to fit a tapering shield); or five forming a cross or saltire. The analogues are obvious.
The ordinaries, too, can be multiple. In hyperheraldry, three or more parallel linear ordinaries need not lie on a plane.