Lissajous curves are graceful patterns formed by combining two perpendicular oscillations, typically one horizontal and one vertical, each varying sinusoidally in time. The exact shape depends on the ratio of their frequencies and the phase difference between them. When the frequencies are equal, the curve may appear as a straight line, an ellipse, or a circle. When the frequencies differ, the path becomes more intricate, producing looping, woven figures that repeat periodically when the ratio i
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Lissajous Love - We created this animation to showcase the beautiful patterns of a Lissajous curve — a path formed when two waves move at right angles with different speeds and rhythms. As they interact, they trace out elegant loops, swirls, and figure-eight shapes that repeat in perfect harmony. Lissajous curves are more than just pretty lines — they reveal the hidden patterns behind motion, music, and even light. In this video, we bring these curves to life, showing how simple math can create
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Lissajous curves are intricate patterns that emerge when two perpendicular harmonic motions are combined—typically one along the x-axis and another along the y-axis, each with its own frequency and phase difference. Depending on the ratio of frequencies, the curves can appear as elegant loops, figure-eights, or complex woven patterns. They were first studied in the 19th century by Jules Antoine Lissajous, who used optical methods with mirrors to visualize the motion. These curves are not only ma
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The math behind beautiful lissajous patterns 😍 #maths #physics #science #mathematics #art #mathart
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