Imaginary Scators Quadratic fractals in Dynamic Space

The scator quadratic iteration in dynamic space [Imaginary Scators Quadratic Mapping In 1+2D Dynamic Space, CNSNS, 2023] has been implemented in the Mandelbulber (version 2.20-dev or more recent) three dimensional fractal visualization program [https://github.com/buddhi1980/mandelbulber2]. Very intricate surfaces are obtained that are difficult to handle by ray tracing programs. The processing power required to generate 3D fractals is greatly increased compared with 2D renderings. It is necessary to extend the two dimensional image grid to three dimensional space. Thus, the iteration of a much larger set of points is required to begin with. Thereafter, computer ray tracing is necessary to establish the observer point of view, with the concomitant occlusion of interior points or points that lie behind a particular surface from the observer point of view. The capability of using parallel GPU processing using OpenCL has greatly enhanced the rendering velocity.
The .fract settings archives can be used to reproduce some of the fractal images published in [Imaginary Scators Quadratic Mapping In 1+2D Dynamic Space, CNSNS, 2023] .

动态空间中的scator二次迭代[Imaginary Scators Quadratic Mapping In 1+2D Dynamic Space, CNSNS, 2023]已在Mandelbulber（2.20-dev及更高版本）三维分形可视化程序[https://github.com/buddhi1980/mandelbulber2]中实现。所生成的曲面极为复杂，难以通过光线追踪（ray tracing）程序处理。相较于二维渲染，生成三维分形所需的计算算力大幅提升。需将二维图像网格拓展至三维空间，因此初始阶段需要对规模大得多的点集开展迭代运算。随后需通过计算机光线追踪确定观察者视角，同时会伴随出现内部点或观察者视角下位于特定曲面后方的点被遮挡的情况。借助OpenCL实现GPU并行运算的功能，极大提升了渲染速度。.fract格式的配置文件可用于复现发表于[Imaginary Scators Quadratic Mapping In 1+2D Dynamic Space, CNSNS, 2023]中的部分分形图像。