What it takes to recreate 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 were remarkably similar to so-called “Chladni figures”: vibrational patterns that arise when sand is sprinkled on a vibrating plate. It seems I wasn’t the only one. British science communicator and YouTube star Steve Mold got so many comments from viewers about the similarities that he decided to test that hypothesis — recreating the title sequence with his own vibration-generated patterns. He documents the journey, and the science associated with it, in the video above. The last recreated title sequence starts at 10:55am.

The phenomenon is technically known as cymatics. In 1680, Robert Hooke experimented with running an arc along flour-coated glass plates to generate vibrations and noticed the telltale knot patterns that formed in the flour. “A rigid plate will have a range of natural resonant frequencies, just like a string, and when the plate is excited at one of these frequencies, it will form a standing wave with fixed nodes,” University of North Carolina physicist Greg Gbur wrote back. in 2013. “These nodes form lines on the slab, as opposed to points on the string.” The flour on the plate made those knot 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 round plates, demonstrating the effect even before Napoleon. The various shapes or patterns created by resonant frequencies are called “Chladni figures” in his honor. Chladni even devised a mathematical formula to predict which patterns would form. The higher the rate of vibration, the more complex those numbers will be. Similar methods are still used in the design of acoustic instruments: for example, violins, guitars and cellos.

Mold’s videos explore a wide variety of topics, including one on the physics of the so-called “chain fountain” (rising self-siphoning beads) that inspired two physicists to test his hypothesis and publish a 2014 paper. Mold also made a hugely popular YouTube video in 2016 about the science behind Chladni figures, which he demonstrated by sprinkling couscous on a large vibrating metal square. So he was a natural person to approach for people who are curious or The rings of power title sequence was made in a similar way.

First, Mold took a closer look at the specific shapes in the title sequence, then tried to figure out how to recreate them (or a similar pattern) using his own vibration plates, along with the transitions between the patterns. There was more to it than little math.

Mold used a program called Desmos to run through different combinations of the two variables at play and the patterns to be produced on a square plate. (He also experimented with a pentagonal plate for contrast.) Many seemed to match patterns in the title sequence quite well. Then he started trying to make those patterns real. “I swept through a huge range of frequencies, found a handful that worked really well, and then I coded something so I could quickly switch between those good frequencies,” says Mold.

The biggest challenge was achieving the signature circle pattern that occurs at some 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 attached in the center so that all the patterns had lines going through that center, which does not move and thus forms part of a node line. But in the actual title sequence, that circle pattern has no lines going through the center. So Mold vibrated the plate from the center instead of running an arc around the edge, as Chladni did.

In the end, Mold came pretty close to the original circle pattern, though he suspects it owes a lot to CGI. “Maybe the whole thing is CGI,” he says in the video. “But if so, I think they’re using simulation software on at least some of it to produce those Chladni figures.”

List image by YouTube/Steve Mold