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The Mandelbrot set stands as one of the most fascinating and visually striking mathematical objects ever discovered, representing a fundamental milestone in dynamical systems theory and fractal geometry. Extending this set into the coquaternionic domain introduces significant mathematical challenges and unveils structures of remarkable complexity. In this work, we investigate the generalization of the Mandelbrot set from the quadratic mapping family \(x^2+b\,x\) in the complex plane to the coquaternionic space \({\mathbb {H}}_\mathrm{{coq}}\) , examining its mathematical properties, visualization techniques, and theoretical implications.

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The Mandelbrot Set for a Coquaternionic Family of Quadratics

  • 会议论文

  • 发表日期：

    2026年

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  • Maria Irene Falcão,
  • Fernando Miranda,
  • Ricardo Severino

摘要

The Mandelbrot set stands as one of the most fascinating and visually striking mathematical objects ever discovered, representing a fundamental milestone in dynamical systems theory and fractal geometry. Extending this set into the coquaternionic domain introduces significant mathematical challenges and unveils structures of remarkable complexity. In this work, we investigate the generalization of the Mandelbrot set from the quadratic mapping family \(x^2+b\,x\) in the complex plane to the coquaternionic space \({\mathbb {H}}_\mathrm{{coq}}\) , examining its mathematical properties, visualization techniques, and theoretical implications.