An Iteration Algorithm for Determination of Fractal Dimensions of Some Fractal Sets
The self-similar set is a limit set associated with an iterated function system and does not depend on initial set. This paper constructs a recurrent sequence associated with the self-similar set, and proves that, the sequence monotonously converges to the fractal dimension of the self-similar
set for any initial value. As a result, a special iteration algorithm is obtained. This algorithm is simpler than Newton's because it does not require the computation of any derivative, and it is more direct than dichotomy because of its monotonicity.
Document Type: Research Article
Publication date: 15 May 2012
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