Bicomplex Burning Ship Fractal
Abstract
This study explores the dynamic behavior of a modified quadratic iteration in the bicomplex number space, incorporating absolute values of components to define the bicomplex Burning Ship fractal. Through idempotent basis decomposition, the four-dimensional dynamical system is reduced to two independent two-dimensional subsystems, enabling a tractable analysis of the fractal’s structure. Visual experiments are conducted using the developed algorithms, and extensive graphical visualizations are generated to examine the structure of the bicomplex Burning Ship. To address the challenge of visualizing a four-dimensional setting, three-dimensional slices are extracted under a specific constraint, providing effective representations of the fractal. As well as the resulting images, three types of conjugation of bicomplex numbers reveal distinctive symmetry properties, unlike the three-dimensional slice of the classical bicomplex Mandelbrot set.
Keywords
Burning Ship, fractals, bicomplex numbers, iteration theory, iterative and com- posite equations
Ethical Statement
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