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<p>This work introduces a novel class of fractional Julia sets incorporating both a short-memory principle and variable-order operators. The resulting sets capture new complex fractal characteristics while maintaining lower computational costs. Visual and numerical analyses illustrate the influence of fractional order and memory length on morphological features, symmetry properties, connectivity patterns, and fractal dimension. Notably, more complex is identified near sensitive parameter values in the short-memory case. Simulations reveal symmetry breaking, connectivity shifts, and dimensional phase transitions that depend on both fractional order and memory length, highlighting the potential of these new mechanisms to extend conventional Julia sets.</p>

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Fractional Julia sets with short memory

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Zining Li,
  • Lu Kong,
  • Yupin Wang

摘要

This work introduces a novel class of fractional Julia sets incorporating both a short-memory principle and variable-order operators. The resulting sets capture new complex fractal characteristics while maintaining lower computational costs. Visual and numerical analyses illustrate the influence of fractional order and memory length on morphological features, symmetry properties, connectivity patterns, and fractal dimension. Notably, more complex is identified near sensitive parameter values in the short-memory case. Simulations reveal symmetry breaking, connectivity shifts, and dimensional phase transitions that depend on both fractional order and memory length, highlighting the potential of these new mechanisms to extend conventional Julia sets.