The market
The global market for base station antennas, fixed outdoor and indoor antennas, was $10 billion in 2009 and is projected to reach $13.3 billion by 2014. Antennas for the defense sector are growing faster than any other, already valued at $1.2 billion with a compound annual growth rate of 13%. Wireless communications have made antennas an indispensable component of computers and microelectronics for residential, commercial, and industrial installations. This wireless telecommunications infrastructure will be worth $2.2 billion by 2014, as every phone, computer, and most homes in the developed world will be equipped with antennas to connect to the internet and mobile phones. Global wireless transmission base stations grew by 17% annually between 2010 and 2011, and multiband antennas grew at a double-digit rate of 39%. China and India are currently the world's largest markets. However, upgrades to European wireless communication systems suggest that Western Europe could experience the strongest growth in the coming years. The German Kathrein Group is Germany's oldest and largest antenna manufacturer, with 6,300 employees and 21 production facilities, and sales exceeding $1.4 billion in 2010. The Putian Antenna Company, a subsidiary of Putian Corporation, is the leading Chinese producer, located in Xi'an, specializing in microwave, mobile, and satellite antennas. Kavveri, headquartered in Bangalore, is the leading Indian competitor, with a manufacturing capacity of one million high-quality antennas per month.
Innovation
The wireless industry has been studying how to manufacture smaller, more powerful antennas with fewer dead zones while improving transmission speeds. The industry is aware of visual pollution and growing consumer awareness of the imminent risks associated with radiation. Standard antennas on the market today resemble ironing boards. The new, smaller version offered by Alcatel-Lucent, the French-American telecommunications equipment manufacturer, looks like a cube, which has the advantage that these receivers and transmitters are small enough to be placed indoors and easily concealed from view. The reduced size of the antennas not only keeps them out of sight, but they also have a greater capacity for transmitting data and voice. Alcatel-Lucent claims that performance will improve tenfold and eliminate the need for all phones to be within two to three kilometers of an antenna. With the arrival of iPhone and data-hungry smartphone users, networks are under strain from the demand. Even the most established service providers are unable to offer 100% quality service, hence the notion and acceptance of "dropped calls," even by the most demanding subscribers. Another major challenge facing the antenna market is interference between different cellular networks. With the increasing number of subscribers in dense urban communication environments such as airports, train stations, conference rooms, and sports stadiums, it has become increasingly difficult for individual service providers to secure clean connections. The only way for antennas to ensure the signal is heard is to "shout" louder, consuming more power. New antenna designs will therefore need to find ways to reduce this "shout," which will ultimately ensure better battery life for all users and reduce power consumption. Johan Gielis excelled in Latin and Greek at the high school in Antwerp, Belgium. He earned a degree in horticulture and, after meeting Jan Oprins, focused his career on bamboo, the tissue culture of giant grasses from tropical and temperate climates. As his research progressed, he experimented with the study of molecular markers and bamboo physiology to try to unravel its metabolism. Since the early 1990s, Johan has been interested in the mathematical modeling of plants, particularly bamboo. In 1994, he began using mathematical formulas to describe natural forms. In 1997, he generalized the "Lamé curves" with a new mathematical formula now known as the "Super Formula." It was first published in 2003 in the American Journal of Botany. Since then, approximately 200 scientific articles have referenced or used the equation that has become known as Gielis's formula. Johan realized that his mathematical breakthrough provides a single equation for calculating any shape in two or three dimensions. The myriad of imaginary geometric shapes, impossible to calculate and conceive with traditional mathematics, are now within reach by working with only six parameters.
The first cash flow
The super formula solves the problem of the limited symmetry of superellipses and supercircles. Shapes like pentagons and starfish, triangles and rose petals, flowers and leaves can now be calculated with a single equation. The ability to calculate shapes in this way has allowed for a rethinking of geometry. Circles and spheres, suspended chains, planetary trajectories, the shape of snowflakes, the outlines of planets and galaxies, radio waves… Waves, telecommunications networks, the formation of rocks and crystals all attempt to optimize surface area, volume, and/or energy. Johan and his team explored the implications of these results for optimization applications such as calculating the shortest distance in networks. He then founded Genicap as a commercial company, operating on a licensing model, and the Simon Stevin Institute of Geometry as a research and teaching center, both with offices in the Netherlands, while maintaining his part-time professorship at the University of Antwerp (Belgium). Building on this foundation, Johan's team, under the direction of Dr. Diego Caratelli, began designing the next generation of antennas, ensuring maximum energy efficiency, the longest possible range, and minimal material usage. With his team, he realized that the Super Formula enables the design of a new class of superformed antennas that can be produced on demand at extremely low cost (one euro cent per unit) while operating in a characteristic ultra-wideband. These antennas can even be made from recycled plastics, eliminating reliance on metals, particularly rare-earth metals. The nature of wireless systems and the interference that can only be overcome by "shouting" and increasing power consumption are driving demand for precise design of improved access points. Since these new antennas can be even smaller, improve radiation patterns, operate with wider bandwidth, and are easy to deploy or install, Johan realized that one of its first commercial applications is the revolutionary design of antennas that bear no resemblance to current shapes. The Genicap team has proven the viability of super antennas. This could mean that the number of repeater towers dotting the horizon could be significantly reduced, dramatically increasing energy and material efficiency. These 3D antennas bear no resemblance to the current cube, ironing board, or pole-like shapes. The successful fabrication of these diatomaceous earth-like structures relies on new technologies such as additive manufacturing and 3D printing (see Case 50). The use of mathematics, geometry and physics to increase productivity and the efficiency of materials and energy is one of the characteristics of the Blue Economy.
The opportunity
The discovery of the Super Formula opens the world to a vast platform of innovation. The sector most likely to be affected is computing. Until now, increasing the performance of computer chips depended on breakthroughs in materials and the physical design of processors. Now, the breakthrough in computing speed is nothing more than the underlying algorithms, which can be significantly simplified using Johan's equation. As visual presentations increasingly move towards 3D, translating a complex image into binary code using the Super Formula can reduce bandwidth by a factor of 100, or even 1,000. This means that simply changing the algorithm unlocks enormous computing power. For the first time, we see how a mathematical formula enables multiple performance improvements without requiring any innovation in materials. The implications are far-reaching. None of the major software companies, whether Microsoft, Oracle, or SAP, have grasped the depth and scope of the Super Formula's impact on their existing core businesses. This, however, presents an opportunity to envision a platform for entrepreneurship that could, over the years, give rise to dozens of new Microsofts. The power of Johan's breakthrough lies in its ability to unleash innovation across everything from computing and communications to packaging and water management, manufacturing, and distribution. It is this kind of innovation that makes the Blue Economy what it is: an opportunity to transform business models in order to shift society toward efficiency, sufficiency, and perhaps even abundance.
