Abstract

An application of optical parallel processing in the generation of fractal images is presented.Iterated function systems [ M. Barnsley, Fractals Everywhere ( Academic, Boston, Mass., 1988), Chap. 3] are the basis of the operation, which can be easily implemented with optical techniques. An optical fractal synthesizer is considered to compute iterated function systems effectively with the advantages of optical processing in data continuity as well as parallelism. As an instance of the optical fractal synthesizer, an experimental system consisting of two optical subsystems for affine transformation and a TV-feedback line is constructed. Several experimental results verify the principle and show the processing capability of the optical fractal synthesizer.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. G. Feitelson, Optical Computing (MIT, Cambridge, Mass., 1988), Chaps. 3, 4, and 6–9.
  2. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983), Chap. 3.
  3. M. Barnsley, Fractals Everywhere (Academic, Boston, Mass., 1988), Chap. 3.
  4. M. F. Barnsley, A. D. Sloan, “A better way to compress images,” Byte 13, 215–223 (1988).
  5. J. P. Crutchfield, “Space–time dynamics in video feedback,” Physica (Utrecht) 10D, 229–245 (1984).
  6. G. Häusler, G. Seckmeyer, T. Weiss, “Chaos and cooperation in nonlinear pictorial feedback systems. 1: Experiments,” Appl. Opt. 25, 4656–4663 (1986).
    [CrossRef] [PubMed]
  7. S. Kocsis, “Digital compression and iterated function systems,” in Applications of Digital Image Processing XII, A. G. Tescher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1153, 19–27 (1989).
  8. J. Stark, “Iterated function systems as neural networks,” Neural Networks 4, 679–690 (1991).
    [CrossRef]
  9. G. Ferrano, G. Häusler, “TV optical feedback systems,” Opt. Eng. 19, 442–451 (1980).
  10. A. W. Lohmann, N. Streibl, “Map transformations by optical anamorphic processing,” Appl. Opt. 22, 780–783 (1983).
    [CrossRef] [PubMed]

1991 (1)

J. Stark, “Iterated function systems as neural networks,” Neural Networks 4, 679–690 (1991).
[CrossRef]

1988 (1)

M. F. Barnsley, A. D. Sloan, “A better way to compress images,” Byte 13, 215–223 (1988).

1986 (1)

1984 (1)

J. P. Crutchfield, “Space–time dynamics in video feedback,” Physica (Utrecht) 10D, 229–245 (1984).

1983 (1)

1980 (1)

G. Ferrano, G. Häusler, “TV optical feedback systems,” Opt. Eng. 19, 442–451 (1980).

Barnsley, M.

M. Barnsley, Fractals Everywhere (Academic, Boston, Mass., 1988), Chap. 3.

Barnsley, M. F.

M. F. Barnsley, A. D. Sloan, “A better way to compress images,” Byte 13, 215–223 (1988).

Crutchfield, J. P.

J. P. Crutchfield, “Space–time dynamics in video feedback,” Physica (Utrecht) 10D, 229–245 (1984).

Feitelson, D. G.

D. G. Feitelson, Optical Computing (MIT, Cambridge, Mass., 1988), Chaps. 3, 4, and 6–9.

Ferrano, G.

G. Ferrano, G. Häusler, “TV optical feedback systems,” Opt. Eng. 19, 442–451 (1980).

Häusler, G.

Kocsis, S.

S. Kocsis, “Digital compression and iterated function systems,” in Applications of Digital Image Processing XII, A. G. Tescher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1153, 19–27 (1989).

Lohmann, A. W.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983), Chap. 3.

Seckmeyer, G.

Sloan, A. D.

M. F. Barnsley, A. D. Sloan, “A better way to compress images,” Byte 13, 215–223 (1988).

Stark, J.

J. Stark, “Iterated function systems as neural networks,” Neural Networks 4, 679–690 (1991).
[CrossRef]

Streibl, N.

Weiss, T.

Appl. Opt. (2)

Byte (1)

M. F. Barnsley, A. D. Sloan, “A better way to compress images,” Byte 13, 215–223 (1988).

Neural Networks (1)

J. Stark, “Iterated function systems as neural networks,” Neural Networks 4, 679–690 (1991).
[CrossRef]

Opt. Eng. (1)

G. Ferrano, G. Häusler, “TV optical feedback systems,” Opt. Eng. 19, 442–451 (1980).

Physica (Utrecht) (1)

J. P. Crutchfield, “Space–time dynamics in video feedback,” Physica (Utrecht) 10D, 229–245 (1984).

Other (4)

D. G. Feitelson, Optical Computing (MIT, Cambridge, Mass., 1988), Chaps. 3, 4, and 6–9.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983), Chap. 3.

M. Barnsley, Fractals Everywhere (Academic, Boston, Mass., 1988), Chap. 3.

S. Kocsis, “Digital compression and iterated function systems,” in Applications of Digital Image Processing XII, A. G. Tescher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1153, 19–27 (1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Fractal generation with an IFS.

Fig. 2
Fig. 2

Conceptual diagram of the OFS.

Fig. 3
Fig. 3

Optical setup of the experimental OFS: BS's, beam splitters; DP's, dove prisms; ZL, zoom lens, L1–L4, lenses; M's, mirrors.

Fig. 4
Fig. 4

Comparison between the fractals calculated (a) by the experimental OFS and (b) by the Sun SPARCStation 2.

Fig. 5
Fig. 5

Fractals obtained by the experimental OFS with the free-running operational mode.

Fig. 6
Fig. 6

Series of fractals obtained by continuous change of the system parameters.

Tables (2)

Tables Icon

Table 1 IFS Code Used for the Fractal Generated in the Clocked Modea

Tables Icon

Table 2 IFS Codes Used for the Fractals Generated in the Free-Running Iteration Modea

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

W i ( X ) = W i [ x y ] = [ a i b i c i d i ] [ x y ] + [ e i f i ] , i = 1 , 2 , , N ,
0 < | a i d i b i c i | < 1 ,
a i = d i ,
b i = c i ,
N = 2 ,
| a 1 d 1 b 1 c 1 | = | a 2 d 2 b 2 c 2 | .
a i = d i ,
b i = c i .

Metrics