Welshapes

Welshapes is a term used in some strands of computational design and geometry to denote a family of decorative planar shapes generated by a simple recursive rule set. The name is said to evoke ornamental motifs associated with Welsh heraldic and Celtic-inspired art, reflecting the emphasis on intricate boundaries and symmetry rather than metric content alone.

Construction and rules: A welshape starts from a seed curve or polygon. A shape grammar rule replaces each boundary edge with a fixed motif that combines a convex arc with a straight segment, then, at each iteration, the motif is applied to every exposed edge. Parameters control curvature, segment length, branching depth, and potential mirroring. Repeating the rule to a chosen depth produces a closed, self-similar boundary that can be scaled or rotated to fit larger designs.

Properties and variants: Welshapes exhibit self-similarity and, when seeded appropriately, bilateral symmetry. The family is tunable by depth, curvature, and branching factors, yielding a continuum from simple geometric ribbons to highly ornate silhouettes. Some variants allow tiling or repeating motifs to cover a plane.

Applications: They appear in decorative graphics, textile patterns, logo design, and educational contexts for teaching recursive generation and shape grammars. An example at depth two yields a motif reminiscent of interlaced patterns.

Status: Welshapes are not a standard mathematical object; rather, they are a design-oriented concept used to illustrate constructive geometry and algorithmic ornament in design literature and classrooms.

See also: shape grammar, fractal, Celtic knot, computational aesthetics.