Abstract
Fractals are used to characterize the dendritic structure in the cast alloys. In the present paper, this idea is applied to the directional dendrities generated mathematically. For this, a computer program has been developed which can generate dendrites with varying arm spacings. Any number of levels such as primary, secondary, tertiary, etc., can be generated. It is found that the "Fractal Dimension" increases linearly on logarithmic scale as the dendrite arms spacing decreases. Traditionally, dendrite arm spacing has been correlated with cooling rate during solidification. This work suggests that the cooling rate, in turn, may be related to the fractal dimension of the dendritic structure. The advantage of fractals over measurement of dendritic arm spacing is that fractal dimension is obtained as an average number representative of the given dendritic structure. On the other hand, dendritic arm spacing measurement, in a given case, is limited to one level only, i.e., either primary, secondary or tertiary dendrite arms. In addition, the arm spacing may vary locally and the estimation of an average value may be difficult. For the real cases, the method can easily be implemented on an image analysis system.