Quantitative Analysis of Geometrical Irregularity for Several Bowls

— 1st Report, Quantitative Analysis and Transcription of Geometrical Irregularity of Relaxation —

Abstract

In order to evaluate the relaxation and surface irregularity of the famous artist’s bowl and other analytical objects, an analytical procedure was developed by applying the concept of fractals, a hyperbola model of the Richardson effect, and FFT analysis. The main results of this study are summarized as follows: (1) To evaluate the irregular surface of relaxation quantitatively, an analytical system using a high-resolution laser sensor was developed, and an analytical-procedure-developed mesh method was established. (2) It was found that the famous artist’s bowl has a fractal nature and a relative self-similarity in wide resolution ranges. (3) The geometrical irregularity of the surface can be effectively evaluated by combining the fractal dimension D and the FFT parameters. (4) In order to apply the design of a mechanical structure in a later study, the target value of the fractal dimension was estimated as D=2.33.