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<p>Inspired by the Weierstrass function, a continuous function with two unbounded variation points defined on the closed unit interval has been constructed, and its fundamental properties are verified. Fractal dimension analysis reveals that while the Hausdorff dimension of its graph is 1, the upper and lower Box dimensions lie within a specific interval. This dimensional non-equivalence elucidates the influence of dual unbounded variation points on fractal complexity.</p>

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A fractal function with double unbounded variation points

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • X. X. Sun,
  • Y. S. Liang

摘要

Inspired by the Weierstrass function, a continuous function with two unbounded variation points defined on the closed unit interval has been constructed, and its fundamental properties are verified. Fractal dimension analysis reveals that while the Hausdorff dimension of its graph is 1, the upper and lower Box dimensions lie within a specific interval. This dimensional non-equivalence elucidates the influence of dual unbounded variation points on fractal complexity.