Hausdorff measure of Sierpinski gasket generated by normal hexagon

Rongfei Xu
2018 Nonlinear Sci. Lett. A   unpublished
In this paper, the Sierpinski gasket (S) generated by a unit normal hexagon is constructed in R 2. The set S is self-similar and is generated by six contractive functions whose compression ratio is 1/6 , and the open set condition(OSC) is satisfied. The Hausdorff dimension of S is equal to its self-similar dimension, its dimensional value is 1. However, the exact value of its Hausdorff measure is 2 by the mass distribution principle. Possible application of Hausdorff dimensions in practice is
more » ... ns in practice is elucidated.
fatcat:af4rincnavgtxbil57gaoubisa