As the system evolves in time, minute changes amplify rapidly through feedback. This means that systems starting off with only slightly differing conditions, rapidly diverge in character at a later stage. Such behaviour imposes strict limitations on predicting a future state, since the prediction depends on how accurately you can measure the initial conditions. When modelling such a system on a computer, just rounding off the decimal points in a different way can radically change the future behaviour of the system. Looking beyond their curious mathematical properties, chaos theory has an immense attraction because of the role it plays in understanding heart failure, meteorology, economics, population biology, neural networks, arrays of parallel processors, leukemia, brain rhythms and gold futures.
Scientists now have an interpretive tool for describing many of the complexities of the world.
Fractal geometry has been used to create images and models of many different areas. Most systems that confront the engineer are nonlinear dynamical systems. Even the flooding of the Nile is being investigated. Many of the shapes mathematicians had discovered generations before are useful approximations of living tissue, clouds and galaxies. Visualization was extended to the physical world.