Corpus ID: 119681083

Fractal Geography of the Riemann Zeta Function

@article{King2011FractalGO,
  title={Fractal Geography of the Riemann Zeta Function},
  author={Chris King},
  journal={arXiv: Dynamical Systems},
  year={2011}
}
  • C. King
  • Published 28 March 2011
  • Mathematics
  • arXiv: Dynamical Systems
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space. 
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References

SHOWING 1-2 OF 2 REFERENCES
Fractals of the Julia and Mandelbrot sets of the Riemann Zeta Function
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and aExpand
On the dynamics of polynomial-like mappings
Applications de type polynomial. Familles analytiques de telles applications. Resultats negatifs. Familles a un parametre d'applications de degre 2. Petites copies de M dans M. Carrottes pour leExpand