Carpet Fractal Geometry

Fractal geometry lies within the mathematical branch of measure theory.

Carpet fractal geometry.

The sierpinsky carpet is a self similar plane fractal structure. The carpet is one generalization of the cantor set to two dimensions. Very broadband and multiband frequency response that derives from the inherent properties of the fractal geometry of the antenna. This article presents the design and development of a compact broadband shaped aperture coupled carpet fractal antenna with a defected ground structure i shaped slot in the ground for broadband ultra wideband uwb and a multiband characteristics.

For optimization simulation have been repeated at various feed positions. The sierpinski carpet has fractal dimension log 8 red carpet fractal by titoinou fractal sierpinski carpet self similar recursive fractal carpet. Blog postings for summer 2010 effectively got put on pause while i worked on a new book alt fractals. The sierpiński carpet is a plane fractal first described by wacław sierpiński in 1916.

The technique of subdividing a shape into smaller copies of itself removing one or more copies and continuing recursively can be extended to other shapes. The sequence starts at upper left with the removal of a central square from a three by three grid of black squares. Fig 2 the sierpinski carpet has fractal dimension log 8 3 red carpet fractal by titoinou on deviantart. 3 1 zero iteration the figures 2 3 and 4 show the simulation results of zero iteration.

A visual guide to fractal geometry and design isbn 09557706831 preview available on google books. From now on any fractal related blogposts will go to the new dedicated alt fractals blog. One way that fractals are different from finite geometric figures is the way in which they scale. Sequence showing the generation of a plane fractal described in 1916 by the polish mathematician waclaw sierpinski 1882 1969.

You keep doing it as many times as you want. Another is the cantor dust. Sierpinski carpet fractal geometry is used and two iterations were performed and simulated using ie3d software 14. By 1918 two french mathematicians pierre fatou and gaston julia though working independently.

For instance subdividing an equilateral triangle. The antenna has overall dimensions of 8 4 cm 5 5 cm 3 2 mm and is fed using aperture coupled feeding mechanism. A dual band antenna using a sierpinski carpet fractal geometry is designed which covers the multiband characteristics of fractals. To construct it you cut it into 9 equal sized smaller squares and remove the central smaller square from all squares.

Fractal antenna is widely used due to the following important facts.