# Technology: Fractals shorten the lines for transmitting videos

By PIYUSH OJHA MATHEMATICIANS in the US have successfully applied fractal geometry in developing a new instrument, called a Video Modem, for transmitting still and moving video pictures over telephone lines. Its speed is fast enough to project video films on a screen. ‘It really is an entirely new technology which we believe will change the way in which computers handle images,’ says Michael Barnsley, one of its creators. Lengthy digital codes are needed to define pictures and other images for use by a computer. A typical picture with a modest resolution of 256 X 256 pixels, or picture elements, after coding for the colour or greyness of each pixel, takes up to 64 kilobytes of space on a disc. Some method for compressing the size of these codes is essential to simplify and to reduce the costs of handling them. Barnsley, with Alan Sloan of Iterated Systems in Georgia, has solved this problem by using fractal geometry. They regard a picture as an assembly of several fractals. Each fractal can be generated by a simple and compact mathematical rule. These rules are devised using a technique based on a mathematical result in fractal geometry, called the collage theorem, which was proved by Barnsley and his colleagues several years ago. Instead of storing the complete digital record of a picture, the Video Modem stores the rules for generating the component fractals and then reconstructs the pictures from these rules whenever it is required. The rules, being compact, require much less storage than the complete pixel-by-pixel record. Once the fractal of a picture is defined, the picture can be reconstructed to any resolution required. The Video Modem consists of two computer boards, an encoder and a decoder, and its associated software. For encoding a sequence of video pictures, a personal computer connected to a video player relays the sequence, one frame at a time, to the encoder. The encoder transforms the picture into fractals and encodes them mathematically; it either stores the fractal codes on a disc or transmits them. Each frame is encoded in two or three seconds. The fractal code of a typical frame of a film requires about 1 kilobyte of storage, compressing the amount of data by a factor of 64. This ratio is smaller, about 20, for a high-quality still frame. The decoder can accept fractal codes either from a disc or from a modem and reconstruct the image on a graphics device. The Video Modem can transmit at a rate of 30 frames of colour pictures per second at a resolution of 256 X 256 pixels, with 8 bits for colour or greyscale, fast enough to project a motion picture on a television screen. Furthermore, these pictures can be reconstructed at a higher resolution than the original. * * * Geometry of fractals A fractal set is a geometrically complex collection of points in a mathematical space in which the notion of near or far has a precise meaning. It is, in fact, very much like a pointillist picture on a piece of rubber. With every fractal,