Origami & Folding
what one sheet can do
Concept

TreeMaker — where it appears

The program implementing the tree method, which turns a stated tree into a crease pattern. It is where the method stopped being a description and became something a designer could run.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

leglegarmarmheadthe checkclosest approach 0.0000no overlap — the packing is validcircles use 71% of the sheetthe rest becomes the bodyefficiency is how much of thesquare the circles can claim,and it is an open problemthe dashed skeleton is the subject; the circles are what it costs

Packing is the hard part

Once a subject is a set of circles, designing the model is fitting them into a square. That step has no general algorithm, no known optimum, and it is where every remaining difficulty in origami design now sits.

design · Circle packing 32 × 32 gridevery crease on a grid line, or at 45°which is why a 64-grid design can be folded at allmountainvalley

Publishing the pattern instead of the sequence

A diagram sequence is one picture per step and a crease pattern is one picture. When designers began releasing patterns rather than diagrams, the cost of publishing a model fell by two orders of magnitude and the difficulty moved onto the reader — which is what made the complex era possible and what made most of it unfoldable.

history · Notation

Named alongside it

The objects these essays reach for when they reach for this one.

Box pleatingCrease patternThe decision problemEfficiencyNotationOptimisationReachabilityRiverTree method

All concepts