The first time I saw the opening credits of The Lord of the Rings: The Rings of Power, I thought the patterns look remarkably like so-called “cladney shapes”: vibrating patterns that form when one scatters sand on a vibrating plate. It seems I’m not the only one. British science lecturer and YouTube star Steve Mold received a lot of feedback from viewers about the similarities, so he decided to test this hypothesis – by recreating the title sequence using his vibration patterns. He documents the journey and associated science in the video above. The final recreated address sequence begins at the 10:55 mark.
This phenomenon is technically known as cymatics. In 1680, Robert Hooke experimented with running an arc along flour-coated glass panes to induce vibrations and observed the telltale nodal patterns that formed in the flour. “A solid plate will have a range of natural resonance frequencies just like a string, and when the plate is excited at one of those frequencies, it will form a fixed wave with fixed nodes,” University of North Carolina physicist Greg Gabor wrote. 2013. “These knots will form lines on the board, as opposed to points on the string.” The flour on the plate made those nodular lines visible.
Eighteenth-century German physicist and musician Ernst Cladney perfected the method 100 years later when he repeated Hooke’s pioneering experiments with circular plates, even showing the effect before Napoleon. The various shapes or patterns created by the resonance frequencies are known as “Cladney Characters” in his honor. Cladney even came up with a mathematical formula to predict what patterns would form. The higher the volatility, the more complex these numbers are. Similar methods are still used when designing acoustic instruments: violins, guitars and cellos, for example.
Mold’s videos explore a variety of topics, including one related to the physics of the so-called “chain fountain” (self-rising drawing beads) that inspired two physicists to test his hypothesis and published a research paper in 2014. Mold also created a video on YouTube Hugely popular in 2016 is about the science behind Chladni’s characters, which he demonstrated by sprinkling couscous on a large vibrating metal square. So he was a normal person to deal with for people who were curious as to whether rings of strength The address sequence is constructed in a similar way.
First, Generator 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 style) using his vibration plates, along with transitions between styles. That involved more than a little math.
The template used a program called Desmos to run through different combinations of play variables and patterns that had to be produced on a square board. (He also tried a pentagon for contrast.) Several people seemed to match fairly well with the patterns in the title sequence. Then he proceeded to try to make these patterns real. “I swept across a wide range of frequencies, found a handful that worked really well, and then coded something up so I could quickly switch between those good frequencies,” Mold says.
The biggest challenge was to achieve the characteristic pattern of the circles that appeared at one point in the sequence. This requires adjusting the boundary conditions to obtain different standing waves at different frequencies. Chladni’s original experiment involved a board that was fixed in the center so that all patterns had lines running through that center, which do not move and are therefore part of the knot line. But in the physical address sequence, this style of circles does not have lines going through the center. The mold vibrated the board from the middle instead of running an arc along the edge, as Cladney did.
In the end, the mold came very close to the original pattern of the circles, although he suspects it owes much to CGI. “Maybe the whole thing is CGI,” he says in the video. “But if that’s the case, I think they’re using simulation software for at least some of them to produce those Cladney numbers.”
Youtube Image List / Steve Generator
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