Buddhabrot

Buddhabrot set is a special visualization method of the Mandelbrot set that focuses on the orbits of points diverging to infinity during the iterative process \( z \mapsto z^2 + c \). Unlike the classical Mandelbrot set, which examines points with convergent orbits, the Buddhabrot maps the probability distribution of passages of individual points along trajectories that escape.

The algorithm iterates over each point in the complex plane and records the positions of its trajectory in a two-dimensional array. For points whose orbits diverge, these passages are counted as the brightness of pixels in the resulting image. The more frequently a trajectory passes through a given point, the brighter the corresponding pixel appears.

This method reveals the intricate dynamic structure of the system, which remains hidden in the standard visualization of the Mandelbrot set. The resulting fractals often resemble abstract images, with increasing brightness and detail as the number of iterations grows.

• Max Iterations: Allows you to set the number of iterations for the visualization.
• Low Color: Defines the color for points with the minimum number of orbit passages.
• High Color: Defines the color for points with the maximum number of orbit passages.
• Reload Button: Re-renders the visualization after parameter values have been changed.