Simple MotionLiving Math Showreel with Glitch Cuts on the Beat
<direction> Make a 20-second motion graphics showreel built entirely from mathematics: every frame is generated from the running time t, with no photos, footage or pictures. Landscape 1920x1080 at 60 fps. It should feel like a precise lab instrument that suddenly becomes beautiful: dark, glowing, exact, with one glitch cut every two seconds on the beat. Eight math scenes play inside a fixed instrument-style frame (corner brackets, wordmark, scene counter and label, beat dot, running clock, progress line, live equation), then an end card with the brand. Avoid grain, stock imagery and any decoration that isn't drawn from the math. </direction> <structure> Cuts at 2, 4, 8, 10, 12, 14, 16 and 18 s, all on beats. 1) 0-2 s, origin: a faint teal ring grows from the centre to r 238 px (0-0.45 s, ease out); axes with ticks every 60 px grow out from a glowing centre point; a ripple ring leaves the point on each beat. A wide-tracked line like "YOUR AI MOTION DESIGNER" resolves from random characters (0.3-0.78 s); a short serif line like "Ideas in motion" types in letter by letter beside the origin (0.5-1.12 s). From 1.35 to 1.95 s a teal arc of r 220 winds once around the origin with a white dot at its tip, and the words fade. 2) 2-4 s, unit circle: a teal circle (r 220) on the left, the angle growing at 4.52 rad/s. White radius, teal cosine leg, pink sine leg, an orange angle arc labelled θ, a dashed pink line to a pink dot at x 820 where the sine is written; the history of the angle trails to the right as a glowing pink sine (104 px per radian) with a faint teal cosine beside it and dotted +1/-1 guides. Live readouts "θ = 4.524 rad" and "sin θ = -0.982". Equation: y = sin θ. 3) 4-8 s, Fourier epicycles: a chain of 180 rotating circles (sorted by size, faint lavender rings, white radii) draws the outline of a big π in glowing orange over 4.3-7.2 s (sine in-out progress), then the shape fills with a soft pink-to-violet gradient while the chain fades. On the left a spectrum of |cₙ| for n = -24...24 (bar heights by the square root of the amplitude) lights up from the centre outward as the drawing progresses; readouts "K = 180 terms" and "t/2π = 0.527". Equation: f(t) = Σ cₙ e^{int}. 4) 8-10 s, a 3D Lissajous knot (sin 3t, sin 2t, sin 5t) traced in 0.6 s, then turning in perspective: a ribbon whose colour runs teal-violet-pink along the curve and whose width and brightness follow depth. On the right a 3x3 grid of small plane Lissajous figures labelled 1:1, 2:3, 4:5, 1:2, 3:4, 5:6, 1:3, 3:5, 3:2 draws in one by one with drifting phase; the last one turns teal inside a thin box. 5) 10-12 s, a wireframe ripple surface z = cos(kr - ωt)/(1 + r) on a 48x48 grid seen from 67° above, revealed outward from the centre in 0.55 s and slowly turning, lines coloured by height from teal through violet to pink. An orange probe dot rides the surface at r = 3.2 with a leader line and live readouts "r = 3.200", "z = 0.276". 6) 12-14 s, a Julia set z² + c filling the frame, opened by a circular portal that expands from the centre with a white rim. c = 0.7885·e^{iα} slides along its circle (sine in-out), so the fractal morphs from separate spirals into a connected shape with a black interior; slow zoom in and rotation. Colours by escape time: indigo, violet, pink, orange, pale cream to white. An inset shows c moving on its circle with "Re c" and "Im c" readouts. 7) 14-16 s, phyllotaxis: 1500 seeds at θₙ = n·137.508°, rₙ = c√n appear from the centre outward and spin, white at first, then pink, violet and teal. On the left φ = 1.6180339887... writes itself digit by digit, a Fibonacci row grows (21 and 34 in teal), with "seeds n = 1500" and "spirals 21 ⟲ 34 ⟳". 8) 16-18 s, Euler's identity: the seeds swirl into a ring that becomes a teal unit circle on the left; a point sweeps from 1 to -1 leaving an orange arc over the top; e^{iπ} appears large, then "+", "1", "=" one by one on the beats, a ring pulses at -1, and "0" lands at 18 s in a pink ring. 9) 18-20 s, end card: the identity shrinks to the top; a big wide-tracked wordmark like "YOUR BRAND" (replace with yours) rises letter by letter from below inside a clip (0.06 s stagger), a teal-violet-pink underline draws across it, a tracked line like "IDEAS IN MOTION × [your web address]" scrambles in, and an italic serif line like "From idea to video in one chat" fades in. Everything fades to black from 19.35 to 19.95 s. </structure> <composition> Background: a deep indigo-black radial glow, centre #10063A fading to #03030A at the edges, no grain. Accents: pink #FB2D89 (main), orange #FE9117, violet #7C6CF2, teal #2DD4B0 and white. Lines and labels in lavender greys: #9A98A4 for labels, #57516F for dim captions, #433E53 for axes. Strokes glow softly with a 12-16 px blur of their own colour. Type: equations in a Computer Modern-like serif (Old Standard TT, variables italic, functions upright); every readout, counter and caption in a monospace (Liberation Mono or similar), small and wide-tracked; the brand name in a bold grotesk with very wide tracking. A fixed frame stays on the whole time, fading in over 0.15-0.9 s: thin corner brackets 27 px long, 47 px in from each corner. Top left: a wordmark like "YOUR BRAND" (bold, 22 px, tracking about 0.35 em) with a tiny tracked line under it like "IDEAS IN MOTION · [your web address]". Top right: a scene counter "01 / 08" and under it a short label per scene, for example "DESCRIBE YOUR IDEA", "EDIT IN WORDS", "NO KEYFRAMES", "3D EFFECTS", "LIVE PREVIEW", "SHAPES AND SOUND", "MUSIC TO THE RHYTHM", "MP4 EXPORT" (replace with your taglines), with a small pink dot to its left. Bottom right: a running clock "t = 03.35 s" (two decimals) and a tiny line with the frame number. Bottom: a 1 px progress line from x 80 to 1840 that fills with a teal-violet-pink gradient as time runs, with small tick marks at every scene boundary. Bottom left: the equation of the current scene. </composition> <techniques> Every cut is a 0.2 s glitch: the outgoing picture is cut into horizontal bands shifted sideways, 3-6 thin full-width lines in teal, pink, orange and white flicker, the whole frame flashes white at about 14% and decays over 0.25 s, and the frame's labels scramble through random characters for a few frames. The pink beat dot flashes bright on every beat and decays over half a beat. The scene's equation fades in 0.1-0.35 s after each cut. Readouts, the clock and the counters update live with the animation. Tracked lines resolve from random characters; serif lines type in letter by letter; the end wordmark rises from below inside a clip with a 0.06 s stagger. Draw-ons and morphs use ease-out or sine in-out progress as given per scene. </techniques> <music> An uplifting electronic track at 120 BPM (piano chords, warm pads, synth bass, four-on-the-floor beat), exactly 20 s long, with every cut landing on a beat. Soft and filtered for the first two seconds with a riser into a boom at 2 s, full drive until 16 s, a filtered breakdown with a riser into a final boom at 18 s, then fading out by 20 s. Mix to about -14 LUFS with true peak below -1 dBTP. </music> <sound> A soft whoosh and three glitch ticks on each cut, and a deeper whoosh and boom when the fractal portal opens at 12 s, all sitting on top of the music on the beat grid. No voice-over. </sound> <references> Math explainer animations crossed with generative creative-coding art and a sci-fi oscilloscope or lab-instrument HUD: thin glowing lines on near-black, monospaced readouts, textbook serif equations. </references>
