Panoramic views of strange attractors

An electronic instrument for displaying any perspective of a three-dimensional surface S generated by three time-varying (not necessarily periodic) signals is described. The surface S is a three-dimensional Lissajous figure which need not be a closed curve as is typical of all strange attractors. This analog (not digital) instrument is designed to rotate S along any axis (not just the X-, Y-, Z-axis) through any prescribed solid angles (0°-360°) in the three-dimensional coordinate system in real time. The instrument works as a preprocessor for a standard oscilloscope and is built with components capable of displaying time-varying signals with a frequency spectrum from 0 to 20 kHz. To illustrate some immediate applications of this instrument, strange attractors associated with both autononmus and nonautonomous circuits are presented in many different perspectives and cross sections. In particular, numerous cross sections of these strange attractors which have never been seen before can be easily displayed in any desired perspective in real time. Such cross sections have proved to be most revealing and invaluable in dissecting and uncovering the fine structures of strange attractors.