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Abstract: In this paper, we analyze the fractal properties of the generalized Chaikin corner-cutting subdivision scheme with two arbitrary parameters. On the basis of the discussion of limit points on the limit curve, the fractal range of the scheme is obtained and illustrated. The results obtained suggest a clear direction for generating fractal curves by using this scheme. Two fractal examples and their complexity evaluation results obtained by using the box dimension are given. [Copyright &y& Elsevier]