Guarding a Koch Fractal Art Gallery

Lauren Cassell; William Roger Fuller

doi:10.4236/ojdm.2012.24026

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OJDM> Vol.2 No.4, October 2012

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Guarding a Koch Fractal Art Gallery ()

Abstract PP. 134-137

DOI: 10.4236/ojdm.2012.24026 4,927 Downloads 7,486 Views

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Lauren Cassell, William Roger Fuller

Affiliation(s)

Department of Mathematics and Statistics, Ohio Northern University, Ada, USA.

ABSTRACT

This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such generalized art galleries are defined. We construct an art gallery in which one side is the Koch fractal and the other sides are three sides of a rectangle. The appropriate measure of coverage by guards is not the total number of guards but, rather, the guards-to-side ratio. We compute this ratio for the cases of shallow and deep versions of the Koch fractal art gallery.

KEYWORDS

Art Gallery Theorem; Koch Fractal; Difference Equation

Cite this paper

L. Cassell and W. Fuller, "Guarding a Koch Fractal Art Gallery," Open Journal of Discrete Mathematics, Vol. 2 No. 4, 2012, pp. 134-137. doi: 10.4236/ojdm.2012.24026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[3]	B. B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman, New York, 1983.

[4]	R. E. Mickens, “Difference Equations: Theory and Applications,” 2nd Edition, Van Nostrand Reinhold, New York, 1990.