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Design Engineering Tip: Don’t move objects at a constant shape. As speed increases, stretch them in the direction of travel. The faster they move, the more they deform. Combined with easing and subtle motion blur, even simple animations can feel significantly more dynamic. const x = useMotionValue(0) const v... show more
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![[Discrete Fourier Transform] by Hand ✍️ In signal processing, the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.](https://image.24vids.com/tw-1805694219031662799/ext_tw_video_thumb/1805693963464327168/pu/img/kOcpELm1j7wfqJlR.jpg)
![Two cinematic prompts for Seedance 2.0 right here 👇 [STYLE + CAMERA + ATMOSPHERE] Ultra-photorealistic cinematic 15-second action sequence from a grounded action thriller film. Nighttime at an abandoned industrial train yard. Old trains, rusted tracks, broken platforms and warehouses. Strong moonlight and industrial lighting. The visual language is gritty and realistic with hyper-realistic practical destruction. Camera is handheld-dynamic with urgent moves. [IMAGE REFERENCES] No reference images provided. Generate a fully consistent lead character: a male fugitive in his mid-30s, short hair, intense expression. He wears a dark jacket, jeans and boots. Maintain exact same appearance and clothing throughout the clip. [TIMELINE SECOND BY SECOND] 0-3s: [Dynamic handheld tracking shot from side-rear] The man runs across the train yard as a freight train derails violently after hitting a collapsed section of track. Massive train cars tip over and crash into the ground, sending metal, wood and cargo flying. The camera tracks him urgently as the destruction spreads. 3-7s: [Slow continuous orbiting camera moving around the frozen destruction] At the peak of the derailment, everything freezes in perfect realistic physics. Huge train cars, twisted metal, wooden debris and clouds of dust hang motionless in the air with accurate weight and trajectories. The camera performs a smooth, continuous orbit through the frozen chaos, moving between large suspended train cars and passing close to sharp metal fragments while the man remains visible. 7-15s: [Dynamic tracking shot as time resumes] At the 7-second mark time snaps back to forward motion with a slight realistic temporal residue. Some outer debris shows a very subtle reverse lag before continuing. The man has used the frozen moment to dive behind a concrete barrier. When motion resumes, several large pieces of metal miss him. He stays low and runs toward an open warehouse as debris finally crashes down. The camera tracks with him through the dust. [STYLE & QUALITY BOOSTERS] Photorealistic 8K, hyper-realistic rigid body destruction with correct material properties (metal, wood, train parts), perfect frozen mid-air physics, seamless transition from freeze to resume, natural dust interaction, heavy cinematic motion blur on fast debris, stable character performance, movie-level practical destruction VFX quality.](https://image.24vids.com/tw-2074131502733152605/amplify_video_thumb/2074096405480620032/img/zUYHavg8GK518E2E.jpg)
![Activate Berserk mode on Seedance 2.0 with this prompt 🤘 [STYLE + CAMERA + ATMOSPHERE] Brutal 2026 Viking action cinema with hyper-realistic grounded fight choreography and heavy physics. Single continuous dynamic tracking shot following a massive fat berserker as he rampages through a Viking village, systematically taking down villagers with brutal force and his axe until he reaches his longhouse, discovers his wife's betrayal and explodes in full berserk rage. Anamorphic lens, subtle film grain, cold northern daylight, intense motion blur, stabilized professional handheld camera. [IMAGE REFERENCES] Generate consistent character: late-30s massive fat but powerfully built Viking berserker, long wild hair and thick beard, intense wild eyes, covered in Norse tattoos and scars, heavy belly but thick muscular arms. Wears dirty fur cloak over bare scarred chest, leather pants, heavy boots and carries a large blood-stained axe. Exact same appearance, body type, clothing and weapon throughout. [TIMELINE SECOND BY SECOND] 0-4s: [Continuous Dynamic Tracking Shot] Camera tracks backward through the muddy village center as the berserker advances with growing rage. Several villagers try to stop him; he swings his heavy axe in brutal arcs, cleaving one and throwing another into a longhouse wall with raw power. Heavy impacts, bodies reacting with realistic weight. Camera tight on his massive frame. 4-8s: [Continuous Dynamic Tracking Shot with subtle lateral orbit] Pushes deeper between longhouses. Uses his massive size to bull-rush and crush one against a post, then delivers devastating axe strikes. Fabric, fur and blood move realistically. Growing intensity. Camera orbits slightly while tracking his advance. 8-12s: [Continuous Dynamic Tracking Shot - Building Rage] Approaches his longhouse area, smashing through a door with his body and axe, throws a villager into a fire pit. His movements become more unhinged. Camera tracks forward as destruction builds. 12-15s: [Continuous Dynamic Tracking Shot - Berserk Explosion] Reaches his longhouse and sees his wife with another man. Full berserk rage erupts. He charges with animalistic fury, axe swinging in devastating blows. Camera stays locked on the explosion of violence as he advances, then slowly pulls back revealing the trail of carnage through the village. Seamless continuous take, peak visceral energy. [STYLE & QUALITY BOOSTERS] Photorealistic 8K, ultra-detailed skin, fabric, fur, wood and blood textures with realistic sweat, dirt and impact, perfect coherent physics on all strikes, throws, body impacts and environmental destruction, flawless motion blur, stable character consistency, no artifacts, professional blockbuster film look, high dynamic range, intense visceral action, cold northern color palette.](https://image.24vids.com/tw-2068834853894664445/amplify_video_thumb/2068833978996387840/img/1cQxAVG9tkD-iZqU.jpg)
![Seedance 2.0 1080p Infinite Fight Scenes From One Prompt Created a parametric prompt for epic fight scenes. You can generate unlimited variations just by changing the parameters. Tested one generation in 1080p with Seedance 2.0 on Higgsfield. More examples with prompts are in the replies. Prompt Template: FORMAT: 15s / continuous fight CHARACTERS A: [character_A] B: [character_B] ENVIRONMENT [short description] FIGHT PROFILE STYLE: [brutal / elegant / tactical / chaotic / cinematic] ENERGY: [low / medium / high / explosive] WEAPONS: [none / melee / mixed] INTENT: [duel / assassination / survival / dominance / training] VISUAL Cinematic realism, physical lighting, shallow DOF, subtle grain, natural motion blur. DIRECTIVE No fixed choreography. Fight emerges dynamically from characters, environment, and momentum. BEHAVIOR - Use environment freely (walls, ground, objects) - Allow verticality (climb, wall-run, elevation shifts) - Encourage unexpected but physically valid actions RULES - Momentum chain only, no isolated actions - Clear positioning at all times - Continuous, motivated camera (POV / OTS / wide / low-high as needed) - Environment actively reacts (splashes, debris, sparks) IMPACT Strong contacts: 2-frame hold + brightness spike + micro shake resume MOTION Secondary delay (~2 frames) on hair, fabric, environment. RHYTHM Fast exchanges + micro pauses + 1–2 slow-motion beats (0.5–1s) ESCALATION Intensity rises. Include: - one vertical/environment-driven move - one decisive high-impact action HERO MOMENT (CRITICAL) Generate one standout finishing beat: - visually dominant, clearly readable - uses environment or full-body motion - slow-motion entry → sharp impact → brief aftermath hold - ends with strong silhouette or positional advantage GUARDRAILS - Keep character identity and position consistent (no teleporting) - Respect weight and inertia (no floaty or impossible motion) - Ensure clear cause → effect in every action - Keep camera readable and motivated (no random spins or cuts) - Use environment logically (no clipping or mismatch) - Prioritize clarity and physical realism over complexity OUTPUT Fluid, physical, cinematic fight with clear spatial logic, dynamic camera, environmental interaction, and a memorable final highlight moment.](https://image.24vids.com/tw-2044830615434854449/amplify_video_thumb/2044829187370835968/img/lg-RjPLd7i2zL9bN.jpg)
![Seedance 2.0 Takeshi's Castle (Roller Game version) prompt 🎎 Authentic 1980s Japanese television game show broadcast footage, realistic recreation of original Takeshi's Castle ENG camera footage, natural handheld camera with subtle shake and tracking, broadcast video noise, analog grain, limited dynamic range and color saturation of the era, slight color bleeding on highlights, chaotic energetic atmosphere of the original show. No reference images provided. Generate the entire scene from the text description. 0-3s: [Wide handheld tracking shot from the side] A determined young Japanese male contestant in his mid-20s, short black hair, wearing a bright orange tracksuit with white stripes, white sneakers and a white headband, sprints confidently from the wooden starting platform onto the first of several large spinning cylindrical logs floating over a murky pond. He runs with pumping arms and focused expression as the log begins to rotate slowly beneath his feet, causing his body to wobble slightly. Water ripples and splashes lightly around the base of the logs. 3-6s: [Dynamic medium tracking shot moving alongside] He leaps to the second spinning log at a slightly higher level, landing with bent knees to absorb the impact. The faster-rotating drum spins his feet out from under him; he flails his arms dramatically to regain balance, torso leaning left then right, face shifting from concentration to surprise. The log's wet surface glistens as he struggles to stay upright. 6-9s: [Closer side profile action shot with motion blur] Pushing forward to the third log, his right foot slips on the spinning wet wood. He lurches forward violently, arms windmilling, body twisting as he tries to recover by crouching low. His left leg dips into the water creating a splash, but he pulls it out and continues with desperate momentum, the rotating cylinder throwing off his rhythm. 9-12s: [Dynamic tracking shot from a three-quarter angle] He attempts a running jump to the next log but the combined spin and his forward speed causes him to lose all balance. His body tilts backward sharply, legs kicking in the air, arms reaching out for nothing as he begins to fall off the side of the log. 12-15s: [Impact focused shot with water dynamics] The contestant falls backward off the spinning log into the pond with a huge explosive splash, water shooting up around his body. He submerges briefly, then resurfaces gasping and flailing, completely soaked, as the logs continue their relentless spinning in the background. His expression is one of shocked defeat mixed with the show's signature comedic failure. High fidelity recreation of 1980s analog broadcast video, visible natural grain and broadcast noise, realistic motion characteristics of old ENG cameras, coherent but slightly imperfect physics and movement as seen in original Takeshi's Castle episodes, era-accurate color response and limited dynamic range, stable character with the natural imperfections of analog footage, no modern digital sharpness or artifacts.](https://image.24vids.com/tw-2072524413061439981/amplify_video_thumb/2072454987184046080/img/lbKvqtzXkdn8Rtrx.jpg)
