The present invention is a compression method for compressing digital data. The data is strings of digital values, which can be broken down to a series of 1's and 0's. The present inventive method uses a chaotic system to compress the data. The first step in the inventive method is generating a plurality of periodic orbits that correspond to a plurality of control bit strings. Each of the periodic orbits is formed with a series of numeric values. The next step is to convert the numeric values of the periodic orbits to digital data values, similar in form to the data to be compressed. The digital data values of the periodic orbits are then organized to identically match the original digital data values. Then the control bit strings corresponding to the organized digital data values of the periodic orbits are identified and saved in order, such that applying the control bit strings to the chaotic system will regenerate the original data.