Labyrinth Fractal on a Convex Quadrilateral
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Labyrinth Fractal on a Convex Quadrilateral

Authors: Harsha Gopalakrishnan, Srijanani Anurag Prasad

Abstract:

Quadrilateral Labyrinth Fractals are a type of fractals presented in this paper. They belong to a unique class of fractals on any plane quadrilateral. The previously researched labyrinth fractals on the unit square and triangle inspire this form of fractal. This work describes how to construct a quadrilateral labyrinth fractal and looks at the circumstances in which it can be understood as the attractor of an iterated function system. Furthermore, some of its topological properties and the Hausdorff and box-counting dimensions of the quadrilateral labyrinth fractals are studied.

Keywords: Fractals, labyrinth fractals, dendrites, iterated function system, non-self similar, non-self affine, connected, path connected.

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References:


[1] L. L. Cristea and B. Steinsky, Curves of infinite length in 4×4 labyrinth fractals, Geom. Dedicata 141, 2009, 1-17.
[2] L. L. Cristea and B. Steinsky, Curves of infinite length in labyrinth fractals, Proc. Edinb. Math. Soc. Ser.L.L. 54(2), 2011 329-344.
[3] L.L. Cristea and Paul Surer, Triangular labyrinth fractals, Fractals, 27(8), 2019, 1950131.
[4] L. L. Cristea and B. Steinsky, Mixed labyrinth fractals, Topology Appl.229, 2017, 112-125.
[5] L. L. Cristea and G. Leobacher, Super-mixed labyrinth fractals, J. Fractal Geom., 2018,
[6] A. A. Potapov, V. A. German and V. I. Grachev, Nano and radar signal processing: Fractal reconstruction complicated images, signals and radar backgrounds based on fractal labyrinths, 14th Int. Radar Symp. (I.R.S.), Dresden, Germany, 941-946, ISSN: 2155-5745.
[7] A. A. Potapov, V. A. German and V. I. Grachev, Fractal labyrinths as a basis for reconstructing planar nanostructures, Int. Conf. Electromagnetics in Advanced Applications (ICEAA), Turin, Italy, 2013, 949-952
[8] A. A. Potapov and W. Zhang, Simulation of new ultra-wideband fractal antennas based on fractal labyrinths, C.I.E. Int. Conf. Radar (RADAR), China, Guangzhou, 2016, 1-5.
[9] A. Potapov and V. Potapov, Fractal radioelements, devices and systems for radar and future telecommunications: Antennas, capacitor, memristor, smart 2d frequency-selective surfaces, labyrinths and other fractal metamaterials, J. Int. Sci. Publ. Mater. Methods Technol., 11,2017, 492-512.
[10] D. Çelik, Y. Özdemir and M. Üreyen, Affine contractions on the plane, International Journal of Mathematical Education in Science and Technology, 38(5),2007, 701-707.
[11] R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Am. Math. Soc., 309, 1988, 811-829.
[12] J.R. Munkres,Topology, Prentice Hall, Inc., Second edition, 1975.