1. A compression method for compressing data having original digital data values, said method using a chaotic system, said method comprising the steps of: generating a plurality of periodic orbits corresponding to a plurality of control bit strings, said periodic orbits having numeric values; converting the numeric values of the plurality of periodic orbits to generated digital data values; matching generated digital data values to original digital data values; identifying the control bit strings that correspond to the matching generated digital data values; and reducing at least one control bit string in the plurality of control bit strings to a smaller substring whereby the smaller substring is substituted in place of the control bit string.