itselfshape

Itselfhape is a term used in geometry and digital design to refer to a class of shapes whose boundary or form is defined in relation to the shape itself. The term does not have a single formal definition and is most often encountered in theoretical discussions, generative art, and experimental graphics.

Conceptually, an itselfshape is created by a self-referential rule. The boundary is produced using a function that depends on attributes of the boundary that has been or will be created. This can be implemented through iterative procedures, where each step revises the boundary based on the current outline, or through implicit definitions that include the shape as a parameter in the equation of a curve or surface.

Construction methods commonly involve iterative refinement: starting from a seed curve and repeatedly applying a rule such as offsetting, smoothing, or re-parameterizing the boundary based on its own geometry; or defining an implicit equation F(x,y,S)=0 where S is the evolving set of boundary points. Computational rendering often uses level-set or mesh-update techniques to realize the evolving boundary.

Examples and scope can be conceptual rather than literal. A circle whose radius at each direction is influenced by properties measured along the boundary, or a closed curve defined by a self-referential condition that links local features to the global shape, illustrate the idea. In practice, implementations are approximations suitable for graphics or design research.

Applications and context: itselfshape is used as a conceptual tool for studying self-reference in geometry and as a design approach in generative art, architectural visualization, and procedural modeling. Related concepts include fractals, self-similarity, and implicit curves.