A new type of impossible objects that become partly invisible in a mirror

Original Paper Area 3

Abstract

This paper presents a new class of anomalous objects that partly disappear when they are reflected in a mirror. They can be constructed by combination of mathematical properties of mirror symmetry and psychological properties of optical illusion. A general method for designing these objects is proposed together with examples.

Keywords

Anomalous object Height reversal Impossible object Optical illusion 

Mathematics Subject Classification

00A66 

Notes

Acknowledgements

This work is supported by the Grant-in-Aide for the Challenging Exploratory Research No. 15K12067 and for the Basic Scientific Research No. 16H01728 of MEXT

References

  1. 1.
    Ernst, B.: Impossible World. Taschen GmbH, Köln (2006)Google Scholar
  2. 2.
    Ernst, B.: The Magic Mirror of M. C. Escher. Taschen GmbH, Köln (2007)Google Scholar
  3. 3.
    Gregory, R.L.: The Intelligent Eye. Weidenfeld and Nicolson, London (1970)Google Scholar
  4. 4.
    Penrose, L.S., Penrose, R.: Impossible objects: a special type of visual illusion. Br. J. Psychol. 49, 31–33 (1958)CrossRefGoogle Scholar
  5. 5.
    Ramachandran, V.S.: Perception of shape from shading. Nature 331, 163–166 (1988)CrossRefGoogle Scholar
  6. 6.
    Sugihara, K.: Machine Interpretation of Line Drawings. The MIT Press, Cambridge (1986)Google Scholar
  7. 7.
    Sugihara, K.: Three-dimensional realization of anomalous pictures: an application of picture interpretation theory to toy design. Pattern Recognit. 30, 1061–1067 (1997)CrossRefGoogle Scholar
  8. 8.
    Sugihara, K.: Design of solids for antigravity motion illusion. Comput. Geom. Theory Appl. 47, 675–682 (2014). doi: 10.1016/j.comgeo.2013.12.007 MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Sugihara, K.: A single solid that can generate two impossible motion illusion. Perception 43, 1001–1005 (2014)Google Scholar
  10. 10.
    Sugihara, K.: Height reversal generated by rotation around a vertical axis. J. Math. Psychol. 68–69, 7–12 (2015). doi: 10.1016/j.jmp.2015.07.001 MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Wade, N.J., Hughes, P.: Fooling the eyes: Trompe lóeil and reverse perspective. Perception 28, 1115–1119 (1999)Google Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.Meiji UniversityKawasakiJapan

Personalised recommendations