An origami Universal Turing Machine design

TL;DR

This paper presents a theoretical design for an origami-based Universal Turing Machine, building on NP-hardness results and origami logic gates, demonstrating the computational universality of origami folding.

Contribution

It introduces a method to construct an origami NAND gate, enabling the creation of a universal Turing machine using origami principles.

Findings

Design of an origami NAND logic gate

Theoretical proof of origami Universal Turing Machine

Extension of NP-hardness results to computational universality

Abstract

It has been known since 1996 that deciding whether a collection of creases on a piece of paper can be fully folded flat without causing self-intersection or adding new creases is an NP-Hard problem (Bern and Hayes). In their proof, a binary state was implemented as a pleat, with the state corresponding to the pleat layering order; states then interact via pleat intersections. Building on some of the machinery of their result, we will present a method for constructing an origami NAND logic gate, leading to a theoretical origami Universal Turing Machine.