Convert anything you draw into a system of epicycles to visualize the discrete Fourier transform.

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

This article provides animated diagrams depicting how different parts of fireworks function. The elements work together through timed mechanisms to produce desired effects.

In this interactive, users can apply layers to various base maps to display natural and human features, including geological activity, biomes, ocean currents, population densities, and light pollution. Custom legends, markers, and drawings can be used to highlight prominent features.

Scientists use the Schrödinger equation to determine how a system governed by a wavefunction—an equation that predicts the probability of certain outcomes—evolves with time. Computers can animate atomic structure and behavior by depicting the wavefunction as a fluid that guides a particle, like water moving a speck of dust.

The shape—called an analemma—can be obtained by photographing the sun from the same location and time daily for a year. The Earth's eccentricity created the analemma's width, and its tilt shifts the sun's height in the sky over the seasons.

DALL-E first uses a model called CLIP to associate pictures with specific words, followed by a model called GLIDE, which slowly removes noise from random dots until a clear image appears that matches the prompt.

Data visualization helps us understand the world, providing a powerful way to communicate complicated information in a quick and efficient way. There are many different ways to create graphs, and these five examples—the pie chart, geographic dot...

The near-infrared and ultraviolet light captured by the space telescope is not visible to human eyes, but observational data of these types of light can be filtered and modified into visible colors. Many detailed images of astronomical objects are the result of combining these artificially colored images into layers.

The discovery of chaos theory came from Edward Lorenz's computer model of the atmosphere, which used three equations to quantify atmospheric circulation. However, the chaotic evolution of this system creates wandering figure-8-like shapes—some resembling butterfly wings—as it repeatedly attempts to settle on one of two values along unique trajectories.

See why seasons exist with this interactive simulator. Toggle between different views of the earth in relation to the sun and watch as the earth's axis causes the sun to shine at different angles throughout the year, causing the weather to fluctuate and more. This simulator clarifies a process many take for granted.

Einstein's theory of general relativity—that mass literally bends space and time—can be difficult for the human brain to imagine. This interactive resource lets you create celestial objects, imagine their effect on space-time, and see how they interact with each other (best viewed on desktop).

The equations apply the laws of thermodynamics, fluid motion, and radiative transfer to a 3D grid along Earth's surface. After solving them for each cell in the grid over a time interval, the results carry over to neighboring cells, and the process repeats into the future.

Coloring books capture the imagination of children and provide them with one of their earliest opportunities for creative expression. This two-minute video shows an augmented reality coloring book app in which children color characters in a printed coloring book, their drawing is detected and tracked, and the video stream is augmented with an animated 3-D version of the character that is textured according to the child's coloring.

When high-energy electrons from particle accelerators are fired into materials like acrylic, they form a charged plane before discharging into scarred patterns within the material. By evenly charging a cylindrical bottle through rotation during the irradiation process, a 3D figure of lightning in a bottle can be created.

In this simulation, users can simulate randomized and preset orbital configurations for up to 10 celestial bodies to observe the system's evolution in an interactive 3D space. The same configurations can produce different orbital behavior—a feature of chaos—by making small changes to an object's mass under advanced settings.

This interactive teaches users to create quantum experiments through lessons resembling video game levels. Users can also use the virtual lab to visualize landmark quantum experiments like entanglement, teleportation, cryptography, and quantum computing, or create their own experiments with drag-and-drop elements.

Artist Michal Levy has chromesthesia, a subtype of synesthesia in which sounds and music trigger involuntary associations with and sensations of color. This condition gives Levy a unique artistic perspective and ability to interact with and interpret music. In this short animation, Levy tries to capture her audiovisual experience of 'Giant Steps," considered a landmark composition in jazz history by musician John Coltrane.

Wind turbines contain a gearbox that increases the rotation of the blades by a factor of 100 from low to high-speed shafts. The latter moves magnets that change the magnetic field within a generator, creating electricity.

Players are tasked with drawing objects, and Google’s AI—which has been trained on millions of user-submitted doodles—tries to guess what’s being sketched. Over 50 million drawings across 345 categories have been created and can be reviewed by users.

When most of us picture a calendar year, we have a foggy image in our minds of the months, in rough, calendar-like grids. But for some folks, that picture is a whole lot more clear. Around 1 percent of the population has a strange ability known as "calendar synaesthesia," which means they're able to visualize in crisp detail an elaborate calendar of the months of the year. Learn how it works here.

Upon retiring, he wanted to get into art, but found the materials to be expensive. Since 2000, he has created art pieces using the line tool and other features the software provides before printing and taping together various spreadsheets that make up a completed work.

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

Various geometric models, including Newton's color circle of hue and saturation and the horseshoe-shaped XYZ space for mixing colors via vector mathematics, have been proposed to describe colors accurately. However, these models do not encapsulate the variety of psychological effects that cause perceived colors to differ from mathematical representations.

Developed during the CERN Summer Student Webfest 2014, this game tasks you with building the reputation of your particle accelerator as you discover particles and hire staff to collect data. A historical breakdown accompanies each discovery, allowing you to recreate the timeline of the field.

Two months in World War I, the newspaper invited readers to sketch postwar borders and submit peace terms for cash prizes. The contest captured public attempts to predict a new world order and foreshadowed modern crowdsourced forecasting. It's a wild look at how uncertain Europe's future was at the time.

Theoretical cosmologist Kip Thorne was consulted and collaborated with the film's visual effects team to develop new rendering software, integrate general relativity, and generate ultra-high-resolution visuals. The results were so accurate, they were published in scientific journals.

It turns out everybody imagines the abstract calendar year in a simple, concrete way, though there are surprising differences between the exact model and shape of each image. Dive into one writer's collection of tens of thousands of questionnaire responses showing the fascinating consistency and divergence of how people visualize time.

Famous astronomer Carl Sagan attempts to describe what it's like to think about the fourth dimension using the famous Flatland example from author Edwin Abbott in this classic video.

In this mathematical system, pi is valued at four, and circles aren't round—they appear as diamonds with corners instead. The system simplifies pixel distances in digital imaging and helps engineers with robot navigation and chip design.

Visualize just how exactly seasons come to be with this animation of the earth in relation to the sun, and see how earth's tilt determines our seasons.

Unlike traditional crystals—whose atomic structures cause them to look identical no matter how you look at them in space—time crystals exhibit this behavior through time, where the motion of atoms will bring them to the same positions relative to one another regularly.

Before the Macintosh, computers were primarily used in offices and required users to type complex commands to perform tasks. Apple followed the device with the LaserWriter printer, bringing graphic production to at-home artists and designers.

The highly popular images produced by the James Webb Space Telescope are an artful collaboration between data science and visual designers. The raw data reflects real physical aspects of space, but it arrives without visual representation. Visual experts assign colors to specific wavelengths, crop and orient images in an accessible way, and consider the emotional impact of images as they incorporate design principles into the final product. Learn the fascinating details here.