The first time I saw the opening credits of The Lord of the Rings: The Rings of PowerI thought the patterns looked remarkably like those called “Chladni figures“: vibrational patterns that form when one spreads sand on a vibrating plate. Looks like I wasn’t the only one. British science communicator and YouTube star steve mold he received so much feedback from viewers about the similarities that he decided to test that hypothesis by recreating the title sequence with his own vibration-generated patterns. He documents the journey and the associated science in the video above. The end sequence of the recreated title begins at the 10:55 mark.
The phenomenon is technically known as cymatics. In 1680, Robert Hooke experimented with drawing an arc across flour-coated glass plates to induce vibrations and noted the telltale nodal patterns that formed in the flour. “A rigid plate will have a set of natural resonance frequencies like a string, and when the plate is excited at one of these frequencies, it will form a standing wave with fixed nodes,” said Greg Gbur, a physicist at the University of North Carolina. wrote in 2013. “These nodes will form lines on the plate, in contrast to points on the string.” The flour on the plate made those nodal lines visible.
18th century German physicist and musician. Ernest Cladni he perfected the method 100 years later when he repeated Hooke’s pioneering experiments with circular plates, even demonstrating the effect before Napoleon. the various shapes or patterns created by resonant frequencies are known as “Chladni figures” in his honor. Chladni even devised a mathematical formula to predict what patterns would form. The higher the wobble rate, the more complex those numbers will be. Similar methods are still used when designing acoustic instruments: violins, guitars, and cellos, for example.
Mold’s videos explore a wide variety of topics, including one on the physics of so-called “chain source” (siphoning up beads) that inspired two physicists to test their hypothesis and publish a paper from 2014. Mold also created a very popular youtube video in 2016 on the science behind the Chladni figures, which he demonstrated by sprinkling couscous on a large vibrating metal square. So he was a natural person to approach for people curious about whether the rings of power The title sequence had been created in a similar way.
Mold first took a closer look at the specific shapes featured in the title sequence, and then tried to figure out how to recreate them (or a similar pattern) using their own vibrating plates, along with the transitions between the patterns. That involved more than a little math.
Mold used a program called Desmos to run various combinations of the two variables in play and the patterns that should be produced on a square plate. (He also experimented with a pentagonal plate for contrast.) Many seemed to match the patterns in the title sequence quite well. He then went about trying to make those patterns real. “I went through a wide range of frequencies, found some that worked really well, and then coded something so I could quickly switch between those good frequencies,” says Mold.
The biggest challenge was achieving the distinctive pattern of circles that appear at one point in the sequence. This required adjusting the boundary conditions to obtain different standing waves at different frequencies. Chladni’s original experiment involved a plate that was fixed in the center so that all patterns would have lines passing through that center, which does not move and is therefore part of a node line. But in the actual title sequence, that pattern of circles doesn’t have lines running through the center. So Mold vibrated the plate from the middle instead of passing an arc along the edge, like Chladni did.
In the end, Mold got pretty close to the original pattern of circles, though he suspects the original owes a lot to CGI. “Maybe it’s all CGI,” he says in the video. “But if it is, I think they’re using simulation software for at least part of it to produce those Chladni figures.”
Listing image by YouTube/Steve Mold