Determination of the apparent fractal dimension of the force-displacement curves of brittle snacks by four different algorithms

The apparent fractal dimension of digitized experimental force-displacement curves of cheese balls and Zwiebacks at various levels of water activity were determined with the Richardson, Minkowski, Kolmogorov and Korcak algorithms. All four, but especially the first three, produced a consistent dimension despite the fact that the curves themselves were nor truly fractal. These calculated dimensions were effective jaggedness measures and could be used interchangeably to monitor moisture sorption effects on the shape of force-displacement relationships. The apparent dimension versus water activity plot had a sigmoid form which was characterized by a shifted Fermi equation. The center point of the jaggedness loss as well as its span was revealed from the magnitude of the equation's constants or directly from the plot.