Modular Origami Halftoning: Theme and Variations

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Zhifu Xiao, Robert Bosch, Craig S. Kaplan and Robert J. Lang: Modular Origami Halftoning: Theme and Variations. In: Bridges 2015. Pages 61–68



We introduce Modular Origami Halftoning, a set of techniques for representing continuous-tone greyscale images using a fixed set of origami modules folded from two-coloured paper. By arranging the modules to reveal different amounts of the paper's coloured side, each module can approximate the brightness of a single pixel from an image. We present two variations based on affixing a grid of disconnected modules to a backing, and one variation in which the modules interlock into a carpet, requiring no tape or glue.

Extended Abstract


 author      = {Zhifu Xiao, Robert Bosch, Craig S. Kaplan and Robert J. Lang},
 title       = {Modular Origami Halftoning: Theme and Variations},
 pages       = {61--68},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{ }},
 url         = { },

Used References

[1] Robert Bosch and Urchin Colley. Figurative mosaics from flexible Truchet tiles. Journal of Mathematics and the Arts, 7(3-4):122–135, 2013.

[2] Kunihiko Kasahara. Extreme Origami. Sterling, 2003.

[3] Ken Knowlton. Ken Knowlton: Mosaics., accessed 3 February 2015.

[4] Meenakshi Mukerji. Marvelous Modular Origami. A K Peters Ltd., 2007.

[5] Al Seckel. Masters of Deception: Escher, Dal´ı & the Artists of Optical Illusion. Sterling, 2007.

[6] Lewis Simon, Bennett Arnstein, and Rona Gurkewitz. Modular Origami Polyhedra. Dover Publications, Mineola, New York, 1999.

[7] Leyla Torres. Origami spirit: Windmill base variations—video. http://www.origamispirit. com/2011/05/windmill-base-variations-video/, accessed 3 February 2015.

[8] Robert Ulichney. Digital Halftoning. The MIT Press, 1987.


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