3D RENDERING OF THE QUATERNION MANDELBROT SET WITH MEMORY
Ricardo Fariello, Paul David Bourke, GABRIEL V. S. ABREU · Fractals · 2024
In this paper, we explore the quaternion equivalent of the Mandelbrot set equipped with memory and apply various visualization techniques to the resulting [Formula: see text]-dimensional geometry. Three memory functions have been considered, two that apply a weighted sum to only the previous two terms and one that performs a weighted sum of all previous terms of the series. The visualization includes one or two cutting planes for dimensional reduction to either [Formula: see text] or [Formula: see text] dimensions, respectively, as well as employing an intersection with a half space to trim the [Formula: see text]D solids in order to reveal the interiors. Using various metrics, we quantify the effect of each memory function on the structure of the quaternion Mandelbrot set.