Crease pattern¶

A planar origami representation that records most or all folds of a finished model in one geometric diagram.

Version: v2 · 2026-09-19 · History
Domain-specific #: 3958
Domain group: Arts & Aesthetic Practice
Origin domain: Art & Aesthetics
Subdomain: Origami Design → Art & Aesthetics

Core Idea¶

A crease pattern marks mountain, valley, boundary, and structural fold lines on the uncreased sheet, encoding the spatial organization from which a folded model can be analyzed or reconstructed. Flattening the model’s fold network into a single sheet diagram preserves adjacency, intersection, angular, and layer-relevant constraints while omitting the temporal folding sequence. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

How would you explain it like I'm…

Map of the Folds

If you make an origami animal and then carefully unfold it, the flat paper shows all the fold lines. A crease pattern is a drawing of those lines, showing which ones fold up and which fold down. It shows where every fold goes, but not the order you fold them in.

Origami Fold Map

A crease pattern is a map of all the folds of an origami model, drawn on the flat, unfolded sheet of paper. It marks which folds are 'mountain' folds (pointing up) and which are 'valley' folds (pointing down), plus the paper's edges and important structural lines. From it, you can figure out how the finished model is built. It doesn't tell you the order to fold things in, like step-by-step instructions do. It just shows where all the folds go and how they fit together.

Single-Sheet Fold Network Diagram

A crease pattern is a diagram of an origami model drawn on the uncreased sheet, showing mountain folds, valley folds, the sheet's boundary, and structural fold lines. It flattens the whole fold network of the finished model onto one sheet, preserving which creases meet, where they intersect, the angles between them, and constraints relevant to how layers stack. It leaves out the time order of folding, so unlike step-by-step diagrams it doesn't say what to fold first. Designers use crease patterns to analyze a model or reconstruct it. A drawing counts as a crease pattern only if it represents a single sheet and its fold network is geometrically compatible with the intended folded shape.

A crease pattern is a single-sheet diagram of an origami design's fold network, marking mountain, valley, boundary and structural creases on the uncreased paper. It is obtained by mapping the folded model's creases back onto the flat sheet, preserving adjacency, intersection and angular relations as well as constraints relevant to layer ordering, while omitting the temporal folding sequence found in step-by-step diagrams. It thereby encodes the spatial organization from which the folded model can be analyzed or reconstructed. For a diagram to count as a crease pattern of a given model, it must correspond to one sheet, record a geometrically compatible fold network, and have its designated creases map to the intended folded structure. A drawing of fold lines that cannot be folded consistently, or that belongs to a different sheet or model, does not qualify.

Scope of Application¶

Crease pattern belongs to origami design and is useful where the analyst can specify the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure. The scope is broad within that domain but bounded by the need for the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Crease pattern can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Crease pattern. Crease pattern compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
Lock the constitutive rule. Express the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of origami design because they reuse the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Flattening the model’s fold network into a single sheet diagram preserves adjacency, intersection, angular, and layer-relevant constraints while omitting the temporal folding sequence., and type the carrier, state every parameter and convention in the definition, test that the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Crease pattern Domain-specific

Parents (1) — outgoing typed relations

Crease pattern is a kind of Representation Prime

What makes it its own entry: the domain-specific identity determined by the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure.

Hierarchy path (1) — routes to 1 parentless root

Crease pattern → is a kind of Representation → presupposes Abstraction

Neighborhood in Abstraction Space¶

Crease pattern sits in a moderately populated region (57^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Scheme Morphisms & Aperiodic Patterns (8 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25