Logic gates and origami? Professor Inna Zakharevich joined us to talk about Turing complete origami crease patterns.
We started talking about Turing completeness which led to a Conway’s Game of Life-like 2D cellular automaton called Rule 110 (Wikipedia) which can be implemented with logic gates (AND, OR, NOT). These logic gates can be implemented as creases in paper (with the direction of the crease indicating 0 or 1).
The paper describing the proof is called Flat Origami is Turing Complete (arxiv and PDF). Quanta Magazine has a summary article: How to Build an Origami Computer.
Inna’s page at Cornell University also has the crease patterns for the logic gates (pdf).
Inna is an aficionado of the origami work by Satoshi Kamiya who creates complex and lifelike patterns.
Some other origami mentioned:
Origami Stegosaurus by John Montroll YouTube Folding video (Part 1 of 3)
Ilan Garibi’s Pineapple Tessellation (PDF instructions)
Eric Gjerde Spread Hex Origami Tessellation (This also has the equilateral triangle grid needed to fold Inna’s gate logic)
Peter Engel
Amanda Ghassaei’s Origami Simulator (Mooser’s is under Examples->Origami)
Some other math mentioned:
Veritasium’s Math's Fundamental Flaw talks about Goerthe’s Incompleteness Theorem
Physical Logic Game: Turing Tumble - Build Marble-Powered Computers
Mathematics of Paper Folding (Wikipedia)
Transcript
476: Sidetracked by Mining the Moon
475: Stuffed Animal or Colleague
473: Math Is Not the Answer
472: Field of Boxes
471: Bicycle Built For Two
470: Upping the Chaos Level
469: Saving the World Is Not a Hobby
468: Designed to Kill All Humans
467: Temporary Axolotl
466: Attacked by a Goose on the Way to the Office
465: Dinosaurs, Pirates, Spaceships
464: Please Make This Monster Look Scary
463: Layers of Band-Aids
462: Spontaneously High Performing
461: Am I the Cow in This Scenario?
460: I Don’t Care What Your Math Says
459: Ideas Have to Come From Somewhere
458: Fiddling, DIY, and Cursing
457: Rubber Duck Phase Cancellation
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