Taylor Approximation ✍️ It shows a mathematical "best guess"... evolving to match a complex 3D shape by adding layers of detail one step at a time. The purple surface is the original goal, while the red grid represents a polynomial approximation anchored at the center point. At first, the red surface can only mimic the very middle of the shape. As the calculation adds more terms, visualized by the red grid rippling and shifting, the approximation "learns" how to curve and bend to match the target more accurately. This is a visual demonstration of how math can break down a detailed, wavy landscape into simpler instructions. When these instructions are stacked together, they recreate the entire surface with incredible precision. Video: mathwithmuzaashow more

Pentagonal Surface flow over water while vibrated by single... tone at 528 hz, affected by a pentagon shape sitting below the surface of the water.show more

A dramatic moment captures a space rock striking the... Moon’s surface, creating a powerful and sudden impact. The object hits at incredible speed, producing a brief flash and disturbing the lunar surface. With no atmosphere to slow it down, the Moon is constantly exposed to impacts from space rocks, which have shaped its cratered landscape over billions of years. Events like this are happening all the time, but capturing one clearly is rare. This moment gives a glimpse into the dynamic nature of space and how even the Moon continues to change. A brief impact, but a powerful reminder of cosmic activity. #nasa #space #spacexshow more

A dramatic moment captures a space rock striking the... Moon’s surface, creating a powerful and sudden impact. The object hits at incredible speed, producing a brief flash and disturbing the lunar surface. With no atmosphere to slow it down, the Moon is constantly exposed to impacts from space rocks, which have shaped its cratered landscape over billions of years. Events like this are happening all the time, but capturing one clearly is rare. This moment gives a glimpse into the dynamic nature of space and how even the Moon continues to change. A brief impact, but a powerful reminder of cosmic activity. #nasa #space #spacexshow more

A dramatic moment captures an asteroid striking the Moon’s... surface, creating a sudden and powerful impact. The object hits at incredible speed, producing a brief flash against the silent lunar landscape. With no atmosphere to slow incoming objects, the Moon experiences direct impacts that shape its cratered surface over time. These events happen more often than we realize, but capturing one clearly is rare. This moment highlights the dynamic nature of space, where even the Moon continues to change through constant impacts. A split-second collision… but a powerful cosmic event.show more

Footage of hypersonic missiles launched by Iran at Israel:... the red color is the result of friction in the atmosphere, these are red trails of "Fateh" hypersonic ballistic missiles in the night sky. The IRGC gives the Israel such a "nighttime beauty", but they don't want to look at it and run to the bunkers - it's a shameshow more

Flame polishing is a method of polishing a material,... usually glass or thermoplastics, by exposing it to a flame or heat.When the surface of the material briefly melts, surface tension smooths the surface.show more

There is a shape in mathematics that can hold... a finite amount of paint, yet would require an infinite amount of paint to coat its surface. It is called Gabriel’s Horn. Imagine rotating the curve y=1/x around the x-axis. The result is a long, tapering surface that stretches infinitely, like a tunnel that never ends. Here’s where the paradox appears. The volume of this shape converges—if you add up all its infinitesimal slices, the total stops growing. In other words, you can completely fill it with a finite amount of paint. But the surface area diverges. No matter how far you go along the horn, there is always more surface to cover. The outer “skin” keeps extending, demanding more paint without end. So while you could pour paint inside and fill it entirely, you would never finish painting the outside. This is not a trick, but a consequence of how infinity behaves. The radius shrinks quickly enough for the volume to remain finite, yet not fast enough to keep the surface area from growing without bound. It reveals a deeper truth: infinity does not simply mean “very large”—it means unending. And sometimes, the infinite can exist within the finite in ways that defy our intuition, even while remaining perfectly consistent in mathematics.show more

🎺 The Gabriel's Horn also known as the Torricelli's... Trumpet is a mind bending geometric paradox where an infinitely long shape encloses a strictly finite volume with an infinitely large surface area. The reason for the juxtaposition lies in the different mathematical rules used to calculate 3D volumes vs 2D surface areas when dealing with exponential quantities to infinity. As the horn stretches out infinitely, its opening gets so narrow that it becomes smaller than the width of a single atom. But the paradox exists only in theoretical math, in the physical world an enclosed volume is proportional to the surface that bounds it. 🔗show more

This is a great example of something that has... to be seen to be believed, and I’m not even talking about the eagles’ amazing aerodynamic abilities. I’m referring to chaotic tidal rapids that cause huge vortexes of water to push fish to the surface. You can clearly see one starting right when the eagle plucks the fish from the surface. The poor fish was rushed to the surface at such a velocity that the air and gases inside it expanded filling it like a balloon. Glad I’m not a fish.show more

The Gaussian Wave Packet ✍️ It is a way... to describe a quantum particle, like an electron, that is located in a certain area of space instead of being spread out everywhere. It forms a bell-shaped curve, where the peak of the curve indicates the most likely place to find the particle. This shape is special because it offers the best way to pack a particle; it meets the physical limit set by the Heisenberg Uncertainty Principle, striking the best balance between knowing a particle's position and its momentum. However, because this packet consists of many different overlapping waves, it is naturally unstable for a free particle. Over time, these internal waves travel at slightly different speeds, which causes the bell curve to gradually flatten and widen. This process is known as dispersion. In simpler terms, the longer a quantum particle travels freely, the more unclear its exact location becomes. Video : Jeedecodeshow more

This animation shows how a uniform grid of points... is deformed by a flow matching model. The visualization highlights how the learned flow warps the underlying space—stretching, compressing, and bending it—to transform one probability distribution into another.show more

This is what the Bedrock Operator sees on a... job site. The camera feed shows what a human operator would see. The LiDAR point cloud shows what the machine knows, the full geometry of the environment, rendered in real time, down to millimeter precision. The excavator's position, the bucket's angle, the shape of the cut: all of it mapped and updated continuously. This is the sensing foundation that makes autonomous operation possible. Before a machine can act safely and accurately, it has to understand its environment completely.show more

i tried Framer Agent to build a brand guidelines... website template, something i've meant to do for a while. a site i can swap a logo, nudge a colour, update the type, and send a link instead of re-exporting a pdf nobody opens. a few observations on the AI process: - i started with references. pulled together a handful of minimalist grid layouts and had Claude describe the visual style back to me. you can do the same inside Framer, feeding it the references directly. - from there i had it write a detailed prompt aimed at that exact style, then asked it to break it into a few smaller steps. then i fed those into the agent, one at a time. - the scaffolding stage is the satisfying part. for something this grid-driven (the columns, the spans, the whole underlying structure) watching it land in seconds is hard to look away from. - but then i still have to sweat the details: text alignment, line-heights, image sizes. i don't mind it at all; it's the part i like, making these design decisions. the strength of the agent is the mundane work. point it at the stuff that eats your time: cleaning up the build, adding responsiveness, dropping in small effects, checking text and colour styles stay consistent, writing alt text for every image. then i get the time back for the parts of web design that are actually fun. 🤝show more

SILENCE REMIX OUT NOW the original is one of... my all time favs.. a true dance classic and to have the honor of adding my touch to it i don’t take lightly.. the goal was to keep the soul of the original while adding a modern production to give this timeless record more life 🙏show more

A better — or at least a more artisanal... — method is to do it by hand using a technique known as pad stitching. This is where the tailor picks up multiple layers of cloth and adds shape using their hands, needle, and thread. Can result in a better lapel roll. IG atelier.willowshow more

Let's take a look at the beautiful vivo OriginOS... 6 ultrasonic fingerprint animation. The feature of this advanced animation is that it can have a relationship with the background and distort the background instead of floating on the surface like Samsung.show more