What it takes to recreate the Rings of Power title sequence with Chladni figures

The first time I saw the opening credits for The Lord of the Rings: The Rings of Power, I found that the patterns looked remarkably like so-called “Chladni figures”: vibration patterns that appear when you scatter sand on a vibration plate. Apparently I wasn’t the only one. British science communicator and YouTube star Steve Mold received so many comments from viewers about the similarities that he decided to test this hypothesis – by recreating the title sequence with his own vibration-generated patterns. He documents the journey and the science involved in the video above. The last newly created title sequence starts at the 10:55 mark.

The phenomenon is technically known as cymatics. In 1680, Robert Hooke experimented with running an arc over flour-covered glass plates to induce vibration and noticed the telltale knot patterns that formed in the flour. “A rigid plate, just like a string, has a natural set of resonant frequencies, and when the plate is excited at one of those frequencies, it forms a standing wave with fixed nodes,” wrote University of North Carolina physicist Greg Gbur in 2013. “These Knots form lines on the plate, as opposed to dots on the string.” The flour on the plate made these nodal lines visible.

The 18th-century German physicist and musician Ernest Chladni perfected the method 100 years later when he repeated Hooke’s pioneering experiments with circular plates and demonstrated the effect even before Napoleon. The various shapes or patterns produced by resonant frequencies are known as “Chladni figures” in his honor. Chladni even developed a mathematical formula to predict which patterns would form. The higher the oscillation rate, the more complex these figures become. Similar methods are still used in the design of acoustic instruments: violins, guitars, and cellos, for example.

Mold’s videos cover a variety of topics, including one on the physics of what’s known as the “chain well” (rising, self-siphoning beads), which inspired two physicists to test his hypothesis and publish a paper in 2014. Mold also created a hugely popular YouTube video about the science behind Chladni figures in 2016, which he demonstrated by sprinkling couscous onto a large vibrating metal square. So he was a natural person to turn to if you were curious if The Rings of Power Title sequence was created in a similar way.

First Mold took a closer look at the specific shapes of 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. There was more to it than just a little math.

Mold used a program called Desmos to go through different combinations of the two in-game variables and patterns to be created on a square sheet. (He also experimented with a pentagonal panel for contrast.) Many seemed to match the patterns in the title sequence quite well. Then he set about making these patterns real. “I searched through a huge range of frequencies, found a handful that worked really well, and then up-coded something so I could quickly switch between those good frequencies,” says Mold.

The main challenge was achieving the distinctive circular pattern seen at one point in the sequence. This required adjusting the boundary conditions to get different standing waves at different frequencies. Chladni’s original experiment involved a plate fixed in the middle, so all patterns had lines going through that middle, which doesn’t move and is thus part of a nodal line. But in the actual title sequence, this circular pattern has no lines going through the middle. So Mold vibrated the plate from the center instead of drawing an arc along the edge like Chladni did.

In the end, Mold came pretty close to the original circle pattern, although he suspects it owes a lot to CGI. “Maybe the whole thing is CGI,” he says in the video. “But if that’s the case, I guess they’re using simulation software for at least part of it to produce these Chladni characters.”

Promotional image from YouTube/Steve Mold