Introduction to Computational Origami by Ryuhei Uehara

Author:Ryuhei Uehara
Language: eng
Format: epub
ISBN: 9789811544705
Publisher: Springer Singapore

We note again that the upper bound by Theorem 6.1.8 and the lower bound by Theorem 6.1.9 differ only by around four times. That is, for most of the MV patterns, the way of folding by the algorithm indicated by Theorem 6.1.8 is almost optimal, and there is little room for improvement. Since these upper and lower bounds depend on the folding model, in order to shrink the constant factor 4, it is necessary to further elaborate the model and make the discussions of both bounds into details.

Anyway, by Theorems 6.1.8 and 6.1.9, most patterns cannot be folded efficiently. That is, patterns such as pleat folding and dragon curve are extremely exceptional special patterns. However, Theorem 6.1.9 shows just existence based on the counting argument, and it does not give specific patterns that cannot be folded efficiently. That is, the following problem is open.

Open Problem 6.1.2

Give a concrete MV pattern where the folding complexity is .

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