Abstract
This paper broadens the research on planar Mandelbrot set to the spatial case by investigating the Mandelbrot set generated in coupled map lattice (CML M-set for short). The visualization and symmetry property of the 3D slice of CML M-set are investigated. Furthermore, a proper controller is designed for the 3D slice of CML M-set to achieve its symmetry change, position change and size change. Numerical simulations are included to verify the effectiveness of the control method.
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