Waves and interference

The rule

A source emits a wave: at each distance d, it sends a value that rises and falls like a cosine, with a period called the wavelength. When several sources are placed on the canvas, none of them wins: at every point, you add up what each one sends there.

value(x, y) = sum, over the sources, of cos(2π · d / λ), where d is the distance from the point to the source and λ the wavelength

Where two crests meet, the values add and the point lights up. Where a crest meets a trough, they cancel and the point goes dark. The drawing is the map of these sums: fringes, rings that cross, patterns that move as soon as a source moves.

To read that map, it is cut into bands of equal width, iso-levels: each band gathers the points whose value is close.

What changes from one algorithm to the next

Moiré Interference

Sources scattered over the canvas each draw evenly spaced concentric circles. Their overlap makes the moiré, and a grid of fine lines can be added behind.

Interference Lattice

Pairs of sources mirrored in twos, sampled on a grid: their waves are added, classically, with no relation to quantum mechanics. A node appears where the amplitude passes a threshold, and its size and colour follow the intensity.

Oil Sheen

The oil film on a puddle. The thickness of the film is a fractal noise, and the light reflected by the top and the bottom of the film recombines according to that thickness: the iridescence follows level curves, they are fringes and not a gradient.

Ectoplasm

Not waves, but a field that also adds up: charges whose contributions are summed. Two neighbouring charges merge, and the nested level curves of their field draw the soft shape of the ectoplasm.