IS PERIODONTAL BREAKDOWN A FRACTAL PROCESS - SIMULATIONS USING THE WEIERSTRASS-MANDELBROT FUNCTION

This paper introduces a theoretical model of periodontal disease that is multifactorial, cumulative and produces periodontal breakdown in '' bursts and remissions''. The simulation is based on the generalization of the Weierstrass-Mandelbrot function as an integration of a series of sinusoid fluctuations that facilitate or prevent periodontal breakd own with different frequencies, amplitudes and phases. The breakdown i s produced when the integration of the factors reaches a certain thres hold and is stopped when it is below it. The zeroset of the function ( the set of points of the function in intersection with the time axis) is a self-similar set that corresponds to the instances when the proce ss switches between destructive and non-destructive phases, and its fr actal nature indicates that in theory, bursts of destruction do not ha ve a characteristic duration size. If the mechanism of periodontal dis ease has in principle similarities to the model presented, then accura te site-specific predictions about periodontal destruction may prove a n unrealizable task.