ingle, compact antenna that can perform all the functions nec- essary to operate AM and FM radios, cellular communications, and navigation systems," says Yahya Rahmat-Samii, who chairs the electrical engineering department at UCLA's Henry Samueli School of Engineering and Applied Science. Fractals, short for "fractional dimension," are mathematical models origi- nally used to measure jagged contours such as coastlines. Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale. Any portion of the curve, when enlarged, appears identical to the whole curve-a property known as "self-symmetry." Rahmat-Samii found that the mathematical principles behind the repetition of these geometrical structures with similar shapes could be applied to a methodology for developing antenna designs. Using this method, he has developed antennas that meet two impor- tant challenges presented by the new generation of wireless devices. They con- serve space and can operate simultaneously at several different frequencies. Fractal methodology allows Rahmat-Samii to pack more electrical length into smaller spaces, he says. Increased electrical length means that the SOMETHING IN THE AIR-RADIO AND LOCATION TECHNOLOGIES antennas can resonate at lower frequencies. Because fractal designs are self- symmetrical (repeat themselves), they are effective in developing antennas that operate at several different frequencies. "One portion of the antenna can resonate at one frequency while another portion resonates at another fre- quency," notes Rahmat-Samii. 6.10.4 Fractal Antenna Design At Pennsylvania State University, researchers are beginning to use fractal theory to design real-world antennas. Engineers have discovered that an antenna design, composed of an array of fractal-shaped tiles, promises to provide a 4:1 to 8:1 improvement in bandwidth compared with their con- ventional counterparts. This concept could lead to a new generation 