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Size distribution of fractal clusters is shown to follow a one-sided stable distribution. Its characteristic exponent α is determined by the fractal relation between the cluster's surface ( S ) and volume ( N ) under the scale change: S → a S , N → a 1/α N . This result means that an asymptotic power law size distribution p ( N )∝ N -α-1 is deduced from the above geometrical fractal relation.
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Hideki Takayasu (1988) studied this question.
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