Orbit Trap Fractals

September 01, 2020

Orbit trap fractals use the same general recurrence function as typical escape-time fractals: z ↦ f(z), calculated over and over. But in the orbit trap method, a region of the image called a "trap” is defined. As the value of z changes ("orbits") with each calculation, if the point lands within the trap region, the pixel will be filled with a color based on how far the point falls from the center of that trap.

The traditional escape-time Mandelbrot set is shown on the left, with the same Mandelbrot equation drawn with an orbit trap along the y-axis on the right.

Many trap shapes are possible, which lead to many interesting results.

Orbit Trap Pseudocode

FOR each pixel (Px, Py) in the image:
    z := complex(Px, Py) scaled to data range
    FOR N iterations:
        # Recurrence function f(z) calculates a new Z
        z := f(z)
        # Orbit traps define the color
        FOR each orbit_trap:
            IF z within trap_area:
                distance := abs(normalized distance to trap_center)
                color := palette[trap_number, iteration, distance]
                IF trap_image[Px, Py] has not been set:
                    # Option - remove above IF and always set color
                    # to reverse trap order
                    trap_image[Px, Py] := color
final_image := composite(all trap_images)

Gallery of Orbit Trap Fractals