This study investigates the reconstruction of self-similar chaotic attractors and virtual functions by mean of fractal interpolation function by choosing vertical scaling parameter as a continuous function on the interval of interpolation. We describe a procedure for the reconstruction of Lorenz attractor and claim that the flexibility on the choice of vertical scaling produce smoother and non-smooth fractal functions which reconstruct the self-affine Lorenz attractor. Apart from approximation and visualization, this paper facilitates fractal function to interact with chaotic systems for proper mild conditions on scaling parameter of fractal functions.

中文翻译：

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基于分数变分形的分形函数寻找自相似混沌吸引子

本研究通过选择垂直缩放参数作为插值区间上的连续函数，利用分形插值函数研究自相似混沌吸引子和虚函数的重构。我们描述了重建Lorenz吸引子的过程，并声称垂直缩放比例选择的灵活性产生了重建自仿射Lorenz吸引子的更平滑和不平滑的分形函数。除了逼近和可视化之外，本文还为分形函数的缩放参数提供了适当的温和条件，从而促进了分形函数与混沌系统的相互作用。