A new result in computational origami design is that any orthogonal maze, with
vertical walls protruding equal heights from a rectangular floor, can be folded
efficiently from a rectangle of paper just a small factor ... (b) 3D extrusion. (c)
Crease ...
Origami Maze Puzzle Font Erik D. Demaine∗
Martin L. Demaine∗
Jason Ku∗
A new result in computational origami design is that any orthogonal maze, with vertical walls protruding equal heights from a rectangular floor, can be folded efficiently from a rectangle of paper just a small factor larger than the floor [DDK10]. The design algorithm has been implemented as a freely available web application:1 you can design a maze or generate one randomly, and the application produces a crease pattern, which you can print and fold into your design. The crease pattern by itself provides a kind of encoding of a maze, which can be decoded by folding. We applied this idea to encode textual messages in crease patterns that can be decoded by folding. Figure 1 shows a simple font we designed with the constraint that each character is a small orthogonal maze, with dimensions between 0 × 2 and 3 × 2. (With larger dimensions, the font might be easier to read, but harder to fold.) Given the crease pattern of a message written in this font, it is a puzzle to decipher the original text. One approach is to print and fold the crease pattern, which provides a physical challenge. Another approach is to fold the crease pattern in your head, providing a mental challenge. A third approach is to treat the pattern as a geometric substitution cipher, look for patterns, and try to match patterns to letters. In the following pages, we provide a series of such puzzles with hidden messages. This font is part of a series of puzzle fonts where reading the message is a puzzle [DDP10], and part of a series of mathematical fonts illustrating a mathematical theorem or open problem [DD03, DDP10]. Puzzle Solutions: nuf evah .5
•
ezam ym daer .4
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tebahpla ezam imagiro .3
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hparg lanog-ohtro yna .2
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9G4G .1
References [DD03]
Erik D. Demaine and Martin L. Demaine. Hinged dissection of the alphabet. Journal of Recreational Mathematics, 31(3):204–207, 2003.
[DDK10] Erik D. Demaine, Martin L. Demaine, and Jason Ku. Folding any orthogonal maze. In Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education, Singapore, July 2010. To appear. [DDP10] Erik D. Demaine, Martin L. Demaine, and Bel´en Palop. Conveyer belt puzzle font. In Proceedings of the 9th Gathering for Gardner, 2010.
∗
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA, {edemaine,mdemaine,jasonku}@mit.edu 1 http://erikdemaine.org/fonts/maze/
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(a) 2D orthogonal maze
(b) 3D extrusion
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(c) Crease pattern
Figure 1: Origami maze alphabet: (c) folds into (b), which is an extrusion of (a). Dark lines are mountain folds; light lines are valley folds; bold lines delineate letter boundaries and are not folds.
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Puzzle 1:
Maze Folder
http://erikdemaine.org/fonts/maze/?text=ANY%20ORTHO-%0AGONAL%20GRAP
Puzzle 2:
Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik. Maze Folder
http://erikdemaine.org/fonts/maze/?text=%20ORiGAMi%0A%20%20%20MAZE%
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Puzzle 3:
Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik.
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4/
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Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik.
Maze Folder
http://erikdemaine.org/fonts/maze/?text=READ%0A%20%20MY%0AMA
Puzzle 4:
Maze Folder
http://erikdemaine.org/fonts/maze/?text=HAVE%0A%20FUN&lock0=true
Check out other mathematical and puzzle fonts. • Feedback or not5: working? Email Erik. Puzzle
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4 Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik.
