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Investigation reveals Hausdorff dimension of the graph in the context of dimension theory, indicating insights into level sets.
In this paper, we investigate the dimension theory of the one-parameter family of Okamoto’s function. We compute the Hausdorff, box-counting, and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set, and we show that for a typical choice of parameter, this value is attained for Lebesgue almost every level set.
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Prokaj et al. (2025) studied this question.
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