of base station antennas and other radio antennas that are smaller and can operate across a wider range of frequencies. Many natural objects, such as tree branches and rivers and their tributar- ies, are versions of mathematical fractals. These designs appear pleasingly irregular to the eye but actually comprise self-similar, repeated units. The new broadband antenna design, developed by the Penn State engineers, is composed of irregular but self-similar, repeated fractal-shaped unit tiles, or "fractiles," that cover an entire plane without any gaps or overlaps. The outer boundary contour of an array built of fractiles follows a fractal distribution. Compared with conventional antennas, fractal antennas have a smaller cross-sectional area, offer wider bandwidth, work without an impedance matching network, and provide higher gain. Building on the fractal antenna concept, Douglas H. Werner, a professor of electrical engineering and senior scientist in Penn State's Applied Research Laboratory, Waroth Kuhirun, Penn State graduate student, and Pingjuan Werner, a Penn State associate profes- sor of electrical engineering have developed a design approach for broadband phased array antenna systems that combine fractal geometry with aspects of tiling theory. The Penn State design exploits the fact that fractal arrays are generated recursively starting from a simple initial unit. Using this characteristic, the researchers were able to develop fast recursive algorithms for calculating radi- ation patterns. Leveraging recursive growth, the researchers were also able to develop rapid algorithms for adaptive beam forming, especially for arrays with multiple stages of growth that contain a relatively large number of elements. "The availability of fast beam-forming algorithms is especially advantageous for designing smart antenna systems," notes Werner. Ultimately, the researchers discovered that a fractile array made of unit tiles based on the Peano-Gosper curve, a specific type of fractal, offers a perform- ance advantage over