Abstract

The historical origins of optical art are traced. The features of the main techniques used by optical artists are discussed from a theoretical point of view. Such techniques include the juxtaposition of colors, three-dimensional projections, the use of optical components, and the application of the moiré technique. An optical theory of the appearance of edges based on the superposition of the after-image is presented. It is suggested that the highly geometrical figures of phosphenes can provide further inspiration for artists.

© 1965 Optical Society of America

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References

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  1. J. Canaday, “Art that Pulses, Quivers and Fascinates”, The New York Times Magazine (21Feb.1965).
  2. B. Rose, “Beyond Vertigo: Optical Art at the Modern”, Art Forum (April1965).
  3. G. Oster in Quasi-Optics, J. Fox, ed. (Wiley-Interscience, New York, 1964), p. 59.
  4. City Art Museum, St. Louis, 20 May–20 June;Seattle Art Museum, 15 July–23 Aug.;Pasadena Art Museum, 25 Sept.–7 Nov.;Baltimore Museum of Art, 14 Dec.–23 Jan. (all 1965).
  5. W. C. Seitz, The Responsive Eye (Museum of Modern Art, New York, 1965).
  6. E. Delacroix, “On Art Criticism”, Revue de Paris (May 1829) (translation by W. Pach, the Marchbanks Press for Curt Valentin, New York, 1946).
  7. C. Yee, Chinese Calligraphy: An Introduction to Its Aesthetics and Technique (Harvard Univ. Press, Cambridge, 1954).
  8. M. Seuphor, Abstract Painting (reprinted by Dell, New York, 1964).
  9. W. Kandinsky, Point and Line to Plane (translation of the 1928 2nd ed.) (S. R. Guggenheim Foundation, New York, 1947).
  10. W. Kandinsky, Concerning the Spiritual in Art (Wittenborn, Schultz, New York, 1947).
  11. R. L. Herbert, ed., Modern Artists on Art (Prentice Hall, Englewood Cliffs, N.J., 1964).
  12. A. Ozenfant, Foundations of Modern Art (new American ed.) (Dover, New York, 1946).
  13. J. Rewald, Georges Seurat (Wittenborn, New York, 1946).
  14. H. Glück, E. Diez, Die Kunst des Islams (IM Propyläen-Verlag, Berlin, 1925).
  15. Leonardo da Vinci, Treatise on Painting, translated and edited by A. P. McMahon (Princeton Univ. Press, Princeton, 1956).
  16. M. Chevreul, The Principles of Harmony and Contrast of Colors and Their Applications to the Arts (Bell, London, 1876), 3rd ed.
  17. O. N. Rood, Student’s Text-book of Color (Appleton, New York, 1881).
  18. J. Itten, The Art of Color (Reinhold, New York, 1961).
  19. D. Katz, The World of Color (Kegan Paul, London, 1935).
  20. J. Albers, Interaction of Color (Yale Univ. Press, New Haven, 1963).
  21. E. G. Boring, Sensation and Perception in the History of Experimental Psychology (Appleton-Century-Crafts, New York, 1942).
  22. R. M. Evans, An Introduction to Color (Wiley, New York, 1948).
  23. E. Heimendahl, Licht und Farbe (de Gruyter, Berlin, 1961).
    [CrossRef]
  24. M. Born, Naturwiss. 50, 29 (1963).
    [CrossRef]
  25. C. Lapicque, Essais sur l’espace, l’art et la destineé (Grosset, Paris, 1958).
  26. I. Meyerson, ed., Problemes de la Couleur (S.E.V.P.E.N., rue du Four, Paris, 1957).
  27. M. Erb, K. M. Dallenbach, Am. J. Psychol. 52, 227 (1939).
    [CrossRef]
  28. G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Barrington, N.J., 1964).This book is accompanied by a set of prints and transparencies to demonstrate the moiré technique.
  29. H. von Helmholtz, Treatise on Physiological Optics, 3rd ed., J. P. S. Southall, ed. (reprinted by Dover, New York, 1962).
  30. J. F. Hochberg, Perception (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  31. M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer, Berlin, 1962).
  32. A. Huxley, Island (reprinted by Bantam Books, New York, 1963), p. 219.
  33. V. Ronchi, Appl. Opt. 3, 437 (1964).
    [CrossRef]
  34. J. S. Friedman, History of Color Photography (Amer. Photographic Publ. Co., Boston, Mass., 1947), Chap. 17.
  35. A. Righi, Nuovo Cimento 21, 203 (1887).
    [CrossRef]
  36. V. Ronchi, La Prova dei Sistemi Ottici (Nicola Zanichelli, Bologna, 1925), Chap. 9.
  37. G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).
    [CrossRef]
  38. G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).
  39. Shown at the Howard Wise Gallery, New York, 5–27 Feb.1965.Accounts of this show are given in, for example, The New York Times (14Feb.1965, p. X17);The New Yorker (25Feb.1965, pp. 24–26);and The Village Voice (18Feb.1965, pp. 9–10).
  40. L. O. Vargardy, Appl. Opt. 3, 631 (1964).
    [CrossRef]
  41. R. Granit, in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. II.
  42. H. Davson, The Physiology of the Eye (Churchill, London, 1949).
  43. D. MacKay, Nature 181, 362 (1958).
    [CrossRef] [PubMed]
  44. J. Keller, Trans. Inst. Radio Eng. AP-4, 312 (1956).
  45. M. Schapiro, Paul Cézanne (Abrams, New York, 1952).
  46. E. Mach, The Analysis of Sensation (translation of the 5th German ed.) (Open Court, Chicago, 1914), pp. 215–220.
  47. F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).
  48. G. Oster, in press.
  49. R. Arnheim, Art and Visual Perception (Univ. of California Press, Berkeley, 1954).
  50. K. Koffka, Principles of Gestalt Psychology (Harcourt Brace, New York, 1935).
  51. C. E. Osgood, Method and Theory in Experimental Psychology (Oxford Univ. Press, New York, 1953).
  52. J. E. Hochberg, V. Brooks, Am. J. Psychol. 73, 337 (1960).
    [CrossRef]
  53. D. F. Fender, Sci. Am. 211, 24 (July1964).
    [CrossRef]
  54. E. R. Jaensch, Eidetic Imagery (Harcourt Brace, New York, 1930).
  55. R. R. Holt, Am. Psychologist 19, 254 (1964).
    [CrossRef]
  56. M. Knoll, J. Kugler, Nature 184, 1823 (1959).
    [CrossRef]
  57. M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
    [CrossRef]
  58. D. Solomon, LSD The Conciousness-Expanding Drug (Putnam’s Sons, New York, 1964).
  59. B. Julesz, Science 145, 356 (1964);Sci. Am. 213, 38 (Feb.1965).
    [CrossRef] [PubMed]
  60. D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination (translated from 1932 German ed.) (Chelsea, New York, 1952).

1965 (3)

J. Canaday, “Art that Pulses, Quivers and Fascinates”, The New York Times Magazine (21Feb.1965).

B. Rose, “Beyond Vertigo: Optical Art at the Modern”, Art Forum (April1965).

G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).

1964 (6)

L. O. Vargardy, Appl. Opt. 3, 631 (1964).
[CrossRef]

V. Ronchi, Appl. Opt. 3, 437 (1964).
[CrossRef]

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).
[CrossRef]

D. F. Fender, Sci. Am. 211, 24 (July1964).
[CrossRef]

R. R. Holt, Am. Psychologist 19, 254 (1964).
[CrossRef]

B. Julesz, Science 145, 356 (1964);Sci. Am. 213, 38 (Feb.1965).
[CrossRef] [PubMed]

1963 (2)

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

M. Born, Naturwiss. 50, 29 (1963).
[CrossRef]

1960 (1)

J. E. Hochberg, V. Brooks, Am. J. Psychol. 73, 337 (1960).
[CrossRef]

1959 (1)

M. Knoll, J. Kugler, Nature 184, 1823 (1959).
[CrossRef]

1958 (1)

D. MacKay, Nature 181, 362 (1958).
[CrossRef] [PubMed]

1956 (1)

J. Keller, Trans. Inst. Radio Eng. AP-4, 312 (1956).

1939 (1)

M. Erb, K. M. Dallenbach, Am. J. Psychol. 52, 227 (1939).
[CrossRef]

1887 (1)

A. Righi, Nuovo Cimento 21, 203 (1887).
[CrossRef]

Albers, J.

J. Albers, Interaction of Color (Yale Univ. Press, New Haven, 1963).

Arnheim, R.

R. Arnheim, Art and Visual Perception (Univ. of California Press, Berkeley, 1954).

Boring, E. G.

E. G. Boring, Sensation and Perception in the History of Experimental Psychology (Appleton-Century-Crafts, New York, 1942).

Born, M.

M. Born, Naturwiss. 50, 29 (1963).
[CrossRef]

Brooks, V.

J. E. Hochberg, V. Brooks, Am. J. Psychol. 73, 337 (1960).
[CrossRef]

Cagnet, M.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer, Berlin, 1962).

Canaday, J.

J. Canaday, “Art that Pulses, Quivers and Fascinates”, The New York Times Magazine (21Feb.1965).

Chevreul, M.

M. Chevreul, The Principles of Harmony and Contrast of Colors and Their Applications to the Arts (Bell, London, 1876), 3rd ed.

Cohn-Vossen, S.

D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination (translated from 1932 German ed.) (Chelsea, New York, 1952).

Dallenbach, K. M.

M. Erb, K. M. Dallenbach, Am. J. Psychol. 52, 227 (1939).
[CrossRef]

Davson, H.

H. Davson, The Physiology of the Eye (Churchill, London, 1949).

Delacroix, E.

E. Delacroix, “On Art Criticism”, Revue de Paris (May 1829) (translation by W. Pach, the Marchbanks Press for Curt Valentin, New York, 1946).

Diez, E.

H. Glück, E. Diez, Die Kunst des Islams (IM Propyläen-Verlag, Berlin, 1925).

Erb, M.

M. Erb, K. M. Dallenbach, Am. J. Psychol. 52, 227 (1939).
[CrossRef]

Evans, R. M.

R. M. Evans, An Introduction to Color (Wiley, New York, 1948).

Fender, D. F.

D. F. Fender, Sci. Am. 211, 24 (July1964).
[CrossRef]

Françon, M.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer, Berlin, 1962).

Friedman, J. S.

J. S. Friedman, History of Color Photography (Amer. Photographic Publ. Co., Boston, Mass., 1947), Chap. 17.

Glück, H.

H. Glück, E. Diez, Die Kunst des Islams (IM Propyläen-Verlag, Berlin, 1925).

Granit, R.

R. Granit, in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. II.

Heimendahl, E.

E. Heimendahl, Licht und Farbe (de Gruyter, Berlin, 1961).
[CrossRef]

Hilbert, D.

D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination (translated from 1932 German ed.) (Chelsea, New York, 1952).

Hochberg, J. E.

J. E. Hochberg, V. Brooks, Am. J. Psychol. 73, 337 (1960).
[CrossRef]

Hochberg, J. F.

J. F. Hochberg, Perception (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Höfer, O.

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

Holt, R. R.

R. R. Holt, Am. Psychologist 19, 254 (1964).
[CrossRef]

Huxley, A.

A. Huxley, Island (reprinted by Bantam Books, New York, 1963), p. 219.

Itten, J.

J. Itten, The Art of Color (Reinhold, New York, 1961).

Jaensch, E. R.

E. R. Jaensch, Eidetic Imagery (Harcourt Brace, New York, 1930).

Julesz, B.

B. Julesz, Science 145, 356 (1964);Sci. Am. 213, 38 (Feb.1965).
[CrossRef] [PubMed]

Kandinsky, W.

W. Kandinsky, Point and Line to Plane (translation of the 1928 2nd ed.) (S. R. Guggenheim Foundation, New York, 1947).

W. Kandinsky, Concerning the Spiritual in Art (Wittenborn, Schultz, New York, 1947).

Katz, D.

D. Katz, The World of Color (Kegan Paul, London, 1935).

Keller, J.

J. Keller, Trans. Inst. Radio Eng. AP-4, 312 (1956).

Knoll, M.

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

M. Knoll, J. Kugler, Nature 184, 1823 (1959).
[CrossRef]

Koffka, K.

K. Koffka, Principles of Gestalt Psychology (Harcourt Brace, New York, 1935).

Kugler, J.

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

M. Knoll, J. Kugler, Nature 184, 1823 (1959).
[CrossRef]

Lapicque, C.

C. Lapicque, Essais sur l’espace, l’art et la destineé (Grosset, Paris, 1958).

Lawder, S. D.

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

Mach, E.

E. Mach, The Analysis of Sensation (translation of the 5th German ed.) (Open Court, Chicago, 1914), pp. 215–220.

MacKay, D.

D. MacKay, Nature 181, 362 (1958).
[CrossRef] [PubMed]

Meyerson, I.

I. Meyerson, ed., Problemes de la Couleur (S.E.V.P.E.N., rue du Four, Paris, 1957).

Osgood, C. E.

C. E. Osgood, Method and Theory in Experimental Psychology (Oxford Univ. Press, New York, 1953).

Oster, G.

G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).
[CrossRef]

G. Oster, in press.

G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Barrington, N.J., 1964).This book is accompanied by a set of prints and transparencies to demonstrate the moiré technique.

G. Oster in Quasi-Optics, J. Fox, ed. (Wiley-Interscience, New York, 1964), p. 59.

Ozenfant, A.

A. Ozenfant, Foundations of Modern Art (new American ed.) (Dover, New York, 1946).

Ratliff, F.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).

Rewald, J.

J. Rewald, Georges Seurat (Wittenborn, New York, 1946).

Righi, A.

A. Righi, Nuovo Cimento 21, 203 (1887).
[CrossRef]

Ronchi, V.

V. Ronchi, Appl. Opt. 3, 437 (1964).
[CrossRef]

V. Ronchi, La Prova dei Sistemi Ottici (Nicola Zanichelli, Bologna, 1925), Chap. 9.

Rood, O. N.

O. N. Rood, Student’s Text-book of Color (Appleton, New York, 1881).

Rose, B.

B. Rose, “Beyond Vertigo: Optical Art at the Modern”, Art Forum (April1965).

Schapiro, M.

M. Schapiro, Paul Cézanne (Abrams, New York, 1952).

Seitz, W. C.

W. C. Seitz, The Responsive Eye (Museum of Modern Art, New York, 1965).

Seuphor, M.

M. Seuphor, Abstract Painting (reprinted by Dell, New York, 1964).

Solomon, D.

D. Solomon, LSD The Conciousness-Expanding Drug (Putnam’s Sons, New York, 1964).

Thrierr, J. C.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer, Berlin, 1962).

Vargardy, L. O.

Vinci, Leonardo da

Leonardo da Vinci, Treatise on Painting, translated and edited by A. P. McMahon (Princeton Univ. Press, Princeton, 1956).

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics, 3rd ed., J. P. S. Southall, ed. (reprinted by Dover, New York, 1962).

Wasserman, M.

Yee, C.

C. Yee, Chinese Calligraphy: An Introduction to Its Aesthetics and Technique (Harvard Univ. Press, Cambridge, 1954).

Zwerling, C.

Am. J. Psychol. (2)

M. Erb, K. M. Dallenbach, Am. J. Psychol. 52, 227 (1939).
[CrossRef]

J. E. Hochberg, V. Brooks, Am. J. Psychol. 73, 337 (1960).
[CrossRef]

Am. Psychologist (1)

R. R. Holt, Am. Psychologist 19, 254 (1964).
[CrossRef]

Appl. Opt. (2)

Art Forum (1)

B. Rose, “Beyond Vertigo: Optical Art at the Modern”, Art Forum (April1965).

Confin. Neurol. (1)

M. Knoll, J. Kugler, O. Höfer, S. D. Lawder, Confin. Neurol. 23, 201 (1963).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature (2)

M. Knoll, J. Kugler, Nature 184, 1823 (1959).
[CrossRef]

D. MacKay, Nature 181, 362 (1958).
[CrossRef] [PubMed]

Naturwiss. (1)

M. Born, Naturwiss. 50, 29 (1963).
[CrossRef]

Nuovo Cimento (1)

A. Righi, Nuovo Cimento 21, 203 (1887).
[CrossRef]

Sci. Am. (1)

D. F. Fender, Sci. Am. 211, 24 (July1964).
[CrossRef]

Science (1)

B. Julesz, Science 145, 356 (1964);Sci. Am. 213, 38 (Feb.1965).
[CrossRef] [PubMed]

The New York Times Magazine (1)

J. Canaday, “Art that Pulses, Quivers and Fascinates”, The New York Times Magazine (21Feb.1965).

Trans. Inst. Radio Eng. (1)

J. Keller, Trans. Inst. Radio Eng. AP-4, 312 (1956).

Other (43)

M. Schapiro, Paul Cézanne (Abrams, New York, 1952).

E. Mach, The Analysis of Sensation (translation of the 5th German ed.) (Open Court, Chicago, 1914), pp. 215–220.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).

G. Oster, in press.

R. Arnheim, Art and Visual Perception (Univ. of California Press, Berkeley, 1954).

K. Koffka, Principles of Gestalt Psychology (Harcourt Brace, New York, 1935).

C. E. Osgood, Method and Theory in Experimental Psychology (Oxford Univ. Press, New York, 1953).

C. Lapicque, Essais sur l’espace, l’art et la destineé (Grosset, Paris, 1958).

I. Meyerson, ed., Problemes de la Couleur (S.E.V.P.E.N., rue du Four, Paris, 1957).

J. S. Friedman, History of Color Photography (Amer. Photographic Publ. Co., Boston, Mass., 1947), Chap. 17.

G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Barrington, N.J., 1964).This book is accompanied by a set of prints and transparencies to demonstrate the moiré technique.

H. von Helmholtz, Treatise on Physiological Optics, 3rd ed., J. P. S. Southall, ed. (reprinted by Dover, New York, 1962).

J. F. Hochberg, Perception (Prentice-Hall, Englewood Cliffs, N.J., 1964).

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer, Berlin, 1962).

A. Huxley, Island (reprinted by Bantam Books, New York, 1963), p. 219.

G. Oster in Quasi-Optics, J. Fox, ed. (Wiley-Interscience, New York, 1964), p. 59.

City Art Museum, St. Louis, 20 May–20 June;Seattle Art Museum, 15 July–23 Aug.;Pasadena Art Museum, 25 Sept.–7 Nov.;Baltimore Museum of Art, 14 Dec.–23 Jan. (all 1965).

W. C. Seitz, The Responsive Eye (Museum of Modern Art, New York, 1965).

E. Delacroix, “On Art Criticism”, Revue de Paris (May 1829) (translation by W. Pach, the Marchbanks Press for Curt Valentin, New York, 1946).

C. Yee, Chinese Calligraphy: An Introduction to Its Aesthetics and Technique (Harvard Univ. Press, Cambridge, 1954).

M. Seuphor, Abstract Painting (reprinted by Dell, New York, 1964).

W. Kandinsky, Point and Line to Plane (translation of the 1928 2nd ed.) (S. R. Guggenheim Foundation, New York, 1947).

W. Kandinsky, Concerning the Spiritual in Art (Wittenborn, Schultz, New York, 1947).

R. L. Herbert, ed., Modern Artists on Art (Prentice Hall, Englewood Cliffs, N.J., 1964).

A. Ozenfant, Foundations of Modern Art (new American ed.) (Dover, New York, 1946).

J. Rewald, Georges Seurat (Wittenborn, New York, 1946).

H. Glück, E. Diez, Die Kunst des Islams (IM Propyläen-Verlag, Berlin, 1925).

Leonardo da Vinci, Treatise on Painting, translated and edited by A. P. McMahon (Princeton Univ. Press, Princeton, 1956).

M. Chevreul, The Principles of Harmony and Contrast of Colors and Their Applications to the Arts (Bell, London, 1876), 3rd ed.

O. N. Rood, Student’s Text-book of Color (Appleton, New York, 1881).

J. Itten, The Art of Color (Reinhold, New York, 1961).

D. Katz, The World of Color (Kegan Paul, London, 1935).

J. Albers, Interaction of Color (Yale Univ. Press, New Haven, 1963).

E. G. Boring, Sensation and Perception in the History of Experimental Psychology (Appleton-Century-Crafts, New York, 1942).

R. M. Evans, An Introduction to Color (Wiley, New York, 1948).

E. Heimendahl, Licht und Farbe (de Gruyter, Berlin, 1961).
[CrossRef]

D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination (translated from 1932 German ed.) (Chelsea, New York, 1952).

D. Solomon, LSD The Conciousness-Expanding Drug (Putnam’s Sons, New York, 1964).

E. R. Jaensch, Eidetic Imagery (Harcourt Brace, New York, 1930).

R. Granit, in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. II.

H. Davson, The Physiology of the Eye (Churchill, London, 1949).

V. Ronchi, La Prova dei Sistemi Ottici (Nicola Zanichelli, Bologna, 1925), Chap. 9.

Shown at the Howard Wise Gallery, New York, 5–27 Feb.1965.Accounts of this show are given in, for example, The New York Times (14Feb.1965, p. X17);The New Yorker (25Feb.1965, pp. 24–26);and The Village Voice (18Feb.1965, pp. 9–10).

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Figures (9)

Fig. 1
Fig. 1

“Metagalaxie” by V. Vasarely (courtesy of Pace Gallery, New York). This work has the aspect of an elastic checkerboard in which indentations, inflations, shears, and torsions have been applied.

Fig. 2
Fig. 2

“Texture Picture” by K. Gerstner (courtesy of Staempfli Gallery, New York). This is a composition of machine-turned metal squares.

Fig. 3
Fig. 3

“White Light Dynamo” by H. Mack (courtesy of Howard Wise Gallery). This piece consists of a corrugated material rotating behind a lenticular glass.

Fig. 4
Fig. 4

“Double Equispaced Circles” by G. Oster (courtesy of Howard Wise Gallery). A moiré pattern of streamers appears when viewed off the perpendicular direction.

Fig. 5
Fig. 5

“Triple Radial” by G. Oster (courtesy of Howard Wise Gallery). Three radial figures give a moiré pattern consisting of dots which appear to float out and twist with slight movement of the observer.

Fig. 6
Fig. 6

“Sinusoidal Prism II” by G. Oster (courtesy of Howard Wise Gallery). A 60° rectangular prism of sinusoidal family of curves. The moiré pattern produced by two faces changes its character with the angle of observation.

Fig. 7
Fig. 7

Designs (moirés and autocorrellations) produced by overlapping the sinusoidal curves of (a). (b) and (c) are with orthogonal displacements. (d) is with 90° rotation.

Fig. 8
Fig. 8

“Baguettes Rouges et Noirs” by J. Soto (courtesy of Kootz Gallery). Rods at various angles suspended in front of parallel lines. The more inclined the rod the greater is the frequency of intersecting “break” points.

Fig. 9
Fig. 9

Possible origin of apparent points on a vertical straight edge. Overlapping of two families of lines representing the diffraction for a vertical edge. One represents the immediate image and the other the rotated after-image. The apex of the moiré pattern produced is in a direction orthogonal to the edge.

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