Fractals in circuits

The relationship between fractals and feedback circuits is discussed. First, fractals are defined as irregular shapes built by the “replacement rule.” Second, three requirements for chaos within a physical system are defined. The paper employs the Tacoma Narrows Bridge system, models its equivalent circuit and simulates it using PSPICE software from MicroSim. This model with its three sub-circuits for negative, zero and positive damping does not represent a chaotic system. The system, although non-chaotic, is graphically visualized using -performance mapping”. The reason for this visualization, in comparison with Julia and Mandelbrot set techniques, is discussed. Finally, fractal information dimension is defined as a measure of complexity and is calculated for each sub-model. It is hypothesized and proven that the unstable model is the most complex and thus yields the higher fractal dimension value. The paper concludes with a final summation of the fractal-feedback circuit relationship