On the noise-perturbed spatial Julia set generated by Lorenz system

This paper extends the study of noise-perturbed planar Julia sets to the spatial case by studying the Julia set of a complex Lorenz system. We give the definition of the Julia set of a complex Lorenz system and visualize its spatial fractal structure. Then, the symmetry property of the 3-D slice of the CLS Julia set is proved. Finally, the influence of additive and multiplicative noises on the CLS Julia set are analyzed with respect to structural damages and changes in symmetry separately.