With the realization that systems such as these existed, attention was shifted to the use of non-linear differential equations which predicted that small changes in some systems could significantly alter the final result of the calculation. The difficulty in this approach is that non-linear equations cannot be solved with methods of analysis. In chaotic systems, erratic, unpredictable randomness is commonplace. These systems include economy, weather and evolution. Mandelbrot Sets Mandelbrot sets were developed as a part of the fractal geometry of Benoit Mandelbrot.
Fractal geometry deals with the formalization of irregularity.
Many natural phenomena posses a scaling property. This occurs when subsections of an object are similar in some sense to the whole of the object. If regions are subdivided into smaller and smaller parts, there is no loss of detail. The set is connected by fine tendrils. While this does naturally occur in nature, for instance in the fjords of Norway, the Mandelbrot sets are a mathematical phenomenon.