Fractal reality of random data compression for equal-interval series

Many natural phenomena of equal-time and/or equal-space interval have been recorded. They exhibited features at many different scales of measurement - suggesting that they could be described as fractals. Two observed terrain elevation data were selected for this study. On the condition that data number was reduced properly, we used the fractal interpolation technique to reconstruct the "original" profile. The random mode was adopted for reducing the measured data. The variations of profiles compared with different ratios of data reduction and several statistics (as the first four moments) were used to test their overall properties. When data compression was as high as 70%, a resembling appearance by means of fractal reconstruction continued to exist. Its excellence appeared on the texture of profile and magnification of visualization.