BI-ASYMPTOTIC FRACTALS - FRACTALS BETWEEN LOWER AND UPPER-BOUNDS

Extending the idea of Rigaut's asymptotic fractals issuing a turnover from a constant to a power-law behaviour towards smaller scales, we ex tend this idea to asymptotic fractals with both lower and upper turnov er points, i.e. the fractal region is terminated, towards larger scale s, by another constant value. This behaviour is typical for natural fr actals, such biological cell boundaries.Here, we present a new analyti c function describing this bi-asymptotic behaviour. The introduced par ameters can be directly interpreted. We show the advantage of this fun ction in fitting processed images of natural and mathematical fractals , in comparison with standard procedures: the determined dimension is significantly more accurate. A program package with this new function is available.