Chaotic data sequences are found in nature in everything from turbulence in the weather to tumor growth in biological systems. Chaotic sequences are the result of non-linear differential equations that govern physical systems, which for years have eluded closed form solution and therefore a coherent, mathematical explanation.
Most advances in chaos theory have resulted with the advent of the computer from the mid-20th century forward because the solutions to these non-linear equations have been found in individual cases with computer simulation of the difference equations that approximate them. The use of these difference equations that approximate chaotic solutions has also found use in the world of encryption, compression and wireless transmission. In these areas it is found that understanding the theory behind non-linear equations may not be as essential as in using its obscure nature to compress or hide data more efficiently.
