Measure, Dimension and Fractals

  • José Luis Del Rio Correa Universidad Autónoma Metropolitana, Unidad Iztapalapa
Keywords: Measure, Dimension, Fractals

Abstract

A pedagogical presentation of the Hausdorff dimension is made, highlighting the way in which Mandelbrot took this highly specialized concept to the natural sciences, where it is generically called the fractal dimension. Some recent applications such as the use of fractal antennas that are more efficient and versatile than the usual ones are also discussed, these antennas are used in cellular telephony and telecommunications, all this caused by the discoveries of Nathan Cohen.

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References

Benoit Mandelbrot How long is the coast of Britain?. Statistical self-similarity and fractional dimension. Science 155, 636-638. 1967. Reproducido en Classics on Fractals. Ed. Gerald A. Elgar, Addison Wesley, 1993.

Lewis Fry Richardson. The problema of contiguity: an appendix of statistic of deadly quarrels. General Systems Yearbook 6, 139-187. 1961.

Felix Hausdorff Dimension und ausseres mass Mathematische Annalen 79, 157-179. 1911 4.- Felix Hausdorff, Dimension and Outer Measure, 1918. Reproducido en Classics on Fractals. Ed. Gerald A. Elgar, Addison Wesley, 1993.

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Abdelati Reha, Abdelkebir El Amri, Othmane Benhmammouch, Ahmed Ou1ad Said. CPW-Fed KOCH SNOWFLAKE Fractal Antenna for UWB Wireless Applications. Transactions on Networks and Communications. August, 2014 Vol.2 Issue 4. DOI: 10.14738/tnc.24.337

Abbas Bin Younas Awan, Zubair Ahmed and Mojeeb Bin Ihsan, "A New High Directivity Fractal Antenna Based on the Modified Koch Snowflake Geometry" Asia Pacific Microwave Conference (APMC 2010) Dec 7-10, 2010, Yokohama Japan. 59

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Published
2018-12-30
How to Cite
Del Rio Correa, J. L. (2018). Measure, Dimension and Fractals. Contactos, Revista De Educación En Ciencias E Ingeniería, (110), 48 - 60. Retrieved from https://contactos.izt.uam.mx/index.php/contactos/article/view/47
Section
Artículos