Abstract
In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.
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Foundation item: the Outstanding Youth Science Foundation of China (59425003)
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Heping, X., Zhigang, F. & Zhida, C. On star product fractal surfaces and their dimensions. Appl Math Mech 20, 1183–1189 (1999). https://doi.org/10.1007/BF02463785
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DOI: https://doi.org/10.1007/BF02463785