Today's video was made in collaboration with HuygensOptics ( [ Ссылка ] ), who is currently running a series of videos on spatial coherence. Part 1 has been published here: [ Ссылка ] and part 2, to which this simulation relates, can be found here: [ Ссылка ]
A couple of weeks ago, Jeroen from Huygens Optics contacted me, to ask whether I would be able to make a video illustrating spatial coherence. It took some trial and error to find appropriate parameter values and tweak the simulation algorithm, but here is the result.
In a small area at the left, 15 sources emit waves. The frequencies and phases of the sources are chosen randomly, with frequencies spread over a small interval.
The aim of the simulation is to show that by interfering, the sources can generate coherent patterns, despite not being synchronized. See the video [ Ссылка ] for more details on coherent structures in waves.
The video has two parts, showing the same simulation with two different color schemes:
Wave height: 0:00
Wave energy (log scale): 1:40
In the first part, the color hue shows the wave height. In the second part, it shows the energy of the wave, averaged from the beginning of the simulation, on a logarithmic scale. There are absorbing boundary conditions on the outer boundaries of the simulation.

Render time: 1 hour 58 minutes
Color scheme: Part 1 - Twilight by Bastian Bechtold
[ Ссылка ]
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
[ Ссылка ]

Music: "Final Reckoning" by Asher Fulero@AsherFulero

See also [ Ссылка ] for more explanations (in French) on a few previous simulations of wave equations.

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper [ Ссылка ]
C code: [ Ссылка ]
[ Ссылка ]
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

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