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infinite distance

Proceedings of the Edinburgh Mathematical Society (1)

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Curves of infinite length in labyrinth fractals
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Ligia L. Cristea, Bertran Steinsky
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 2 / June 2011

Published online by Cambridge University Press:

30 March 2011, pp. 329-344
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We define an infinite class of fractals, called horizontally and vertically blocked labyrinth fractals, which are dendrites and special Sierpiński carpets. Between any two points in the fractal there is a unique arc α; the length of α is infinite and the set of points where no tangent to α exists is dense in α.