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Measuring Complexity

It is of considerable value to be able to classify models accounting to some measure of difficulty, particularly in lists for instruction sheets in our library. If possible, we would prefer an objective method, (i.e., not dependent on the judgement of a person making the assessment) which is simple, but reasonably orders models in terms of difficulty of folding.

Analysis suggests three ways of measuring complexity : I) To count the number of straight lines required to describe the shape (external)

ii) To identify projections from the basic shape and count these only.

(iii) To count the total number of enclosed shapes bounded by either paper edges or a fold on all external surpluses of the finished model.

In order to illustrate the 3 methods I will analyse 5 models (all taken from Randlett's, "Art or Best of Origami"

Hatchet, page 15

Best of Origami


Bunny, page 35 Art of 0rigami . Traditional

Songbird Page 24

Best of 0rigami.

Sam Randlett

Hen, page 155

Best of Origami.

Adolph Cerceda

Elephant ,page 139

Best of Origami

George Rhoads

It is relatively easy to apply the idea of counting straight lines to describe the shape for a model such as the Hatchet where 7 straight lines are required to draw the the external shape. Such a method becomes difficult, if not impossible, where the Songbird's head is concerned or parts of the Hen because the paper is almost being moulded into curves.

Projections from a base shape may be easy for the rabbit but what is the basic shape for the elephant ?

I will therefore try the idea of counting totally enclosed shapes bounded by edges or folds as (iii). Strictly speaking we ought to count both sides (or all sides for a 3D model), since, however, the 5 models here are all symmetric I will count only one side for the sake of simplicity. The actual counts have been listed on the drawings (note there is no special meaning in the way this has been done).

In order we have the following result :

Model Index Count












I think there will be general agreement that this Index gives a sensible order of difficult from the easiest Hatchet to the most difficult (Elephant). It is clear that this index is not a ratio scale, i.e., the Bunny is not necessarily twice as difficult a. the Hatchet; nor is it necessary additive i.e., the Hen is not as difficult as the Bunny and Songbird together. The index almost certainly is useful mainly as an approximate measure of difficulty.

It has been tried on many animal models and seems reasonable. Particularly difficult models to assess are, 3D and where all surfaces must be counted, and even then it is doubtful if the index is valid; and masks which are one-sided and have many 'mould' type folds.Geometric folds may well have a low score and yet require very difficult folding which is hidden away in the final result.

golden crane award