| In this document, we present some distance estimation formulas that can apply both to bicomplex Mandelbrot sets as well as bicomplex Julia sets. These formulas are used to ray trace slices of above mentioned sets in three dimensional space. Moreover, we will also present a hitherto unpublished method to explore and infinitely approach above mentioned 3D fractals.; With recent progress in bicomplex analysis, it is now possible to give rigorous proof of these formulas which have multiple uses. In the following pages they will be used in a ray tracing method, in exploration and shading of fractals.; The reader will notice that the images generated with these results are incredibly beautiful. Moreover, the complexity of these fractals justifies the creation of an exploration method. We will put emphasis on the generalized Mandelbrot set for bicomplex numbers in three dimensional space, and more specifically the Tetrabrot (Fig. 1) because of its rich fractal structure and symmetry.; The theory presented here was developed with bicomplex numbers but can also be applied to other types of numbers or fractals, including Quaternions, Cayley numbers and some fractals with potential function. |
