Glow Trace Tune

Glow Trace Tune gives you a target curve and asks you to rebuild it from spinning circles. The gold curve on screen is your target — a closed shape drawn by a mathematical process that combines rotating circles of different speeds. Your task is to find those circles. A palette of frequencies sits below the canvas: tap one to add a spinning circle at that frequency. Two sliders control it — amplitude sets how large the circle is, phase sets where in the rotation it begins. As you adjust either, a blue reconstruction curve updates live on screen. The gold ghost and your blue attempt are always visible simultaneously. The gap between them is the puzzle. The mathematics behind this is the Fourier series. Every closed curve — every shape at all — can be expressed as a sum of rotating circles, each spinning at a whole-number multiple of a base speed. A circle spinning once per period contributes a round loop. A circle spinning twice contributes a distortion. A circle spinning four times, added to one spinning once, creates a three-lobed trefoil, because the difference in frequencies — four minus one equals three — determines how many lobes appear in the combined path. A circle spinning six times, added to one at the right phase, creates a five-pointed star. The shape is encoded in the frequencies. Finding the frequencies is the puzzle. The spinning orrery is always visible — the mechanical system of circles within circles, each attached to the tip of the previous one, all turning simultaneously at their own speeds. The outermost tip leaves a glowing trail. Watching it trace the target curve when the frequencies are right is one of the most visually satisfying moments in any puzzle game — the impression that the universe is a clock, and you have finally wound it correctly. At low difficulty the target contains a single frequency. The task is simply tuning the amplitude of one circle until it matches the target radius. At medium difficulty two frequencies are required, and the interaction between them — how amplitude and phase of each affects the combined shape — demands genuine spatial reasoning. At hard difficulty three or more frequencies interlock, and finding the right combination requires understanding that odd harmonics produce symmetric shapes, that high frequencies create fine detail on a coarser base shape, that phase shifts rotate contributions without changing their magnitude. When the reconstruction matches the target above eighty-eight percent, both curves simultaneously shift to white and pulse — a merging flash that holds for a moment before fading. The orrery's circles all brighten together. This is the confirmation that the frequencies have been found, that the shape has been decomposed, that a curve which looked arbitrary has been revealed as a specific, exact combination of rotating circles. This is the same mathematics Ptolemy used to describe planetary motion in 100 AD. It is the same mathematics that compresses JPEG images by discarding high-frequency components. It is how MRI machines reconstruct tissue density from frequency measurements. It is how audio synthesisers build any imaginable timbre from sine waves. Glow Trace Tune makes it tangible before it makes it formal, which is the only order in which it can be genuinely understood. No ads. No timers. No prior knowledge of mathematics required. The curves show you everything. The frequencies are there to be found. Just the gold ghost, the spinning circles, and the moment the two become one.