itselfshapes

Itselfshapes is a coined term used to describe a class of geometric figures defined by self-reference. In this concept, a shape's construction rules are intrinsic to the shape itself rather than external parameters.

Formally, itselfshapes can be viewed as fixed points of a shape-generating operator. If F maps a shape to a new outline by applying its creation rule, a shape S is an itselfshape when F(S) = S, or when S encodes the rule required to generate S.

Common construction methods include recursive subdivision where each iteration uses the current outline to produce the next, L-system based generation in which production rules reference the current shape, and implicit or parametric descriptions that self-contain the equation of the boundary.

In practice, they appear in generative art and mathematical explorations of self-reference, fixed points, and emergence. They serve as a design space for illustrating how a shape can describe and produce itself, rather than relying on external templates.

See also self-similarity, recursion, fractals, fixed point theory, generative art, procedural generation.