Guide Fractal geometries

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Contents:
  1. Fractal Geometry and Stochastics 6
  2. Contact Professor Jawad K. Ali
  3. Horizons of Fractal Geometry and Complex Dimensions
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Fractal Geometry and Stochastics 6

Access provided by: anon Sign Out. Design of wideband fractal antenna with combination of fractal geometries Abstract: A new small size fractal antenna is proposed for the application in wide-band frequency range. It is designed with the combinations of two fractal geometries. The wideband mechanism is explored by investigating the behaviour of the current on the patch.


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The length and width of Koch and cantor fractal geometries are optimized to achieve a wide bandwidth. The feed circuit is a microstrip line with a matching section over a rectangular ground plane.

The measured dB reflection bandwidth for frequency range 1. Measurements done for different purposes suggest that this region's D lies around 2.

Contact Professor Jawad K. Ali

And most of the more formal material is relegated to a forty-page "Mathematical Backup and Addenda". It is not a popular work, however, as it assumes a solid familiarity and comfort not just with mathematical ideas and ways of thinking but with concepts from physics such as percolation, dissipation, and power laws. It is not inaccessible to students or lay readers, but the intended audience is mathematicians and mathematically aware scientists. Some historical background is woven into everything, but thirty five pages at the end add some details.


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Some "Historical Sketches" explore earlier premonitions and dead-ends and half-starts. And Mandelbrot includes a brief account of his own "path to fractals".

Fractals are typically not self-similar

A sixteen page colour insert constitutes a self-contained essay on the history of fractals in art and visualisation. The graphics of The Fractal Geometry of Nature , here and in the black and white illustrations accompanying the main text, were superb for their time but now seem relatively ordinary.

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Horizons of Fractal Geometry and Complex Dimensions

Some of Mandelbrot's terminological suggestions — such as trema for the "holes" or "gaps" removed in the construction of fractals — have clearly failed to get traction. And a huge amount of work has been done both on the mathematics of fractal geometry and on its application. But otherwise The Fractal Geometry of Nature has survived thirty years surprisingly well.