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Interactive visualization of quaternion Julia sets

Published: 23 October 1990 Publication History

Abstract

The first half of a two-step quaternion Julia set visualization system is described. This step uses a quaternion square root function to adapt the classic inverse iteration algorithm to the quaternions. The augmented version produces a 3-D Julia set defined by a point cloud that can be interactively manipulated on a graphics workstation. Several cues are assigned to the point cloud to increase depth perception. Finally, a short theorem is proven that extends the domain of the inverse iteration method to a rotational family of quadratic quaternion Julia sets.

References

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W. R. Hamilton. Elements of Quaternions, volume 1--2. Chelsea Publishing Company, New York, 3rd edition, 1969.
[2]
J. C. Hart. Image space algorithms for visualizing quaternion Julia sets. Master's thesis, EECS Dept., University of Illinois at Chicago, 1989.
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J. C. Hart, D. J. Sandin, and L. H. Kauffman. Ray tracing deterministic 3-D fractals. Computer Graphics, 23(3):289--296, 1989.
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J. A. R. Holbrook. Quaternionic astroids and starfields. Applied Mathematical Notes, 8(2):1--34, 1983.
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J. A. R. Holbrook. Quaternionic Fatou-Julia sets. Annals of Science and Math Quebec, 1987(1):79--94, 1987.
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B. B. Mandelbrot. Fractal aspects of the interation of z → λz (1-z) for complex λ and z. Annals New York Academy of Sciences, 357:249--259, 1980.
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B. B. Mandelbrot. The Fractal Geometry of Nature. Freeman, San Francisco, 2nd edition, 1982.
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A. Norton. Generation and rendering of geometric fractals in 3-D. Computer Graphics, 16(3):61--67, 1982.
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A. Norton. Julia sets in the quaternions. Computers and Graphics, 13(2):267--278, 1989.
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H. -O. Peitgen and P. H. Richter. The Beauty of Fractals. Springer-Verlag, New York, 1986.
[11]
H. -O. Peitgen and D. Saupe, editors. The Science of Fractal Images. Springer-Verlag, New York, 1988.

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cover image ACM Conferences
VIS '90: Proceedings of the 1st conference on Visualization '90
October 1990
501 pages
ISBN:0818620838

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IEEE Computer Society Press

Washington, DC, United States

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Published: 23 October 1990

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VIS90
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VIS90: Visualization '90
October 23 - 26, 1990
California, San Francisco

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