Chaos and fractals from third‐order digital filters

Abstract It is observed that the third‐order digital filter with an overflow non‐linearity has a much richer dynamics than the second‐order digital filter. Computer simulations show that the third‐order non‐linear system can exhibit incredibly complicated fractal geometrical patterns. A three‐dimensional trajectory of the non‐linear system always lies on several parallel planes, but reaches these planes at different points to create the chaotic behaviour and the fractal geometrical patterns. the number and location of the planes are determined by the parameters of the system and the starting point of the trajectory. In general, a seven‐value symbolic dynamics is developed to explain the complex dynamics observed in the non‐linear digital filter.