Visualize how data becomes organized through a variety of sorting algorithms

An overview of 12 fundamental types of algorithms and the uses for each

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

Traffic flow can be improved through research into card shuffling

Card-shuffling mathematics has been applied to solving problems in biology to estimate the evolutionary distance between organisms and in computer science to determine the optimal distribution of files and folders in databases.

Algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

Visualize chaos with the orbit of three or more objects bound by gravity

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.

A breakdown of algorithms, how they are constructed, and their applications

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

Explore a visualization of the data behind Ben & Jerry's legendary ice cream flavors.

An interactive periodic table maps every possible combination of cheese variables

Plotting milk type, texture, rind, mold, aging, and processing as intersecting axes, the tool shows which combinations already exist as named cheeses, which survive only as rare regional styles, and which remain entirely unexplored.

Besides the periodic table, there are over 1,000 alternative ways to organize the known elements, with many arrangements emphasizing specific trends among them.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

Watch an animated visualization of how the Large Hadron Collider works, including how particles are accelerated through a series of machines and how collision data is collected and distributed worldwide.

Test your gerrymandering skills with this interactive game

This simulation demonstrates how packing and cracking alter election outcomes. See how shifting district lines can change representation—regardless of the overall makeup of the electorate.

Explore an optical table to create quantum physics experiments

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.

See how computer memory really works—from binary bits to modern RAM

The video explains how computers store information as 1s and 0s, how RAM functions as fast working memory, and why systems utilize different types of storage. The video demonstrates how this process enables computers to operate.

Explore an interactive history of Google search trends

This interactive allows users to browse for the most searched topics on Google Search since 1999 and provides noteworthy statistics. Topics are sorted by categories, including athletes, movies, reality TV, dog breeds, and sauces.

Five charts that changed the world

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...

How algorithmic redistricting works

Computational methods are convincing a number of judges that some state district maps are drawn illegally. Here's a simple overview of how it works.

Compression algorithms can reduce file sizes without losing quality by consolidating repeated data or replacing blocks of code with more compact representations, thereby reducing storage demands and improving data transmission rates.

An explanation of Turing machines—the foundations of digital algorithms and computers

The device reads data, overwrites or ignores it, and then moves on to the next piece of data based on a set of programmed rules. By imagining this data as zeros and ones—binary that makes up computer code—Turing machines became the theoretical models for how any algorithm could be run on a computer if the procedure could be coded into a set of digital rules.

With many smaller computing cores, graphics processing units process many identical tasks in parallel, whereas central processing units have fewer, larger cores built to handle a wide variety of more complex tasks sequentially.

Explore a visually captivating, interactive animation that lets users click through anxiety-inducing scenarios, make choices, and see the repercussions.

Visualizing cause of death over time in America

As people age, their life expectancy decreases, but the timing and speed of this decline have evolved over the years. Check out this chart which shows the shift in various causes of death of Americans over the last few decades. Data from the...

Visualize the components of fireworks

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

Visualizing the 75 largest underwater animals

With so many fish in the sea, which are the largest? This infographic shows fantastic illustrations of the 75 largest sea animals, ranked by average size. The detailed visual is organized in descending order of size, starting with the blue whale,...

Advance genetic research by playing these scientific video games

Computers produce so much information that researchers can't properly analyze all the data produced, and the overload can also lead computers to make mistakes. Researchers are increasingly turning to citizen scientists—members of the public who are willing to volunteer—to help them make sense of data when computers can't. This article details a few of the ways you can contribute to genetics research by playing video games.

Explore an interactive periodic table of each element's history, properties, and uses.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

It took 70 years for computer scientists to determine how to cut a cake fairly

The cake-cutting problem explores how to divide something fairly, which is not solely about cutting evenly-sized pieces. A protocol that accounted for personal preferences (e.g., a corner piece) between just three people took 16 years to develop.

Explore over 30,000 Olympiad-level math problems from around the world.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Explore an interactive visualization of the solar system

This tool allows you to view the orbits of planets, dwarf planets, moons, asteroids, and other significant objects in the solar system. Clicking on an object reveals key facts and historical data.

Explore the effects of tornadoes of different scales

In this simulation, users can adjust the tornado's diameter and rotation speed to see its impact as it passes through a series of trees and a one-story home.

Visualizing 100 years of Pulitzers

This fascinating data visualization breaks down a century of Pulitzer Prizes. Award categories are laid out against a timeline, and the symbols used to represent each winner indicate the topic of the winning work; the number of prizes won by that outlet thus far; and whether the prize was awarded to an individual or a newsroom. For the best viewing experience, zoom in using the magnifying glass on the cursor until it hits full-screen mode.

View a ranking of research institutions, filterable by region, country, research area, or journal group.

Learn how the algorithms behind Tinder, Bumble, Hinge, and other dating apps work

Formerly based on the Elo rating system, which ranks chess players, the Tinder algorithm is built on user data, with more time spent on the app providing more data on user preferences from which to customize potential matches. OkCupid's match percentage algorithm relies on overlaps in users' search preferences and responses to a subset of over 4,000 questions.

Explore data on every US county with this interactive

The Community Explorer is an interactive tool that brings the power of big data and machine learning to the equity-related policy discussion. Search by economic profile and county and see the country from a different lens.

Experimenting with space-time

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).

View an infographic of the Standard Model

Much like this visualization, the theory serves to catalog almost all phenomena involving visible matter comprehensively, including organizing observed elementary particles by shared characteristics and explaining most fundamental forces and quantum properties.

Explore a visual guide to how quantum computers can crack RSA encryption

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

All computers are defined by their ability to input, store, process, and output data

From wooden machines to wearable tech, computers have changed a lot in appearance, but they all still perform the same essential tasks. Early computers were made of wood and metal—some were so big that they filled entire rooms just to solve simple math problems.

Bias can manifest in algorithmic decisions because the program follows rules that may have been written by individuals unaware of their own biases.

The origin of shortest-path algorithms and how they became optimized for navigation apps

In 1956, Dutch programmer Edsger Dijkstra spent about 20 minutes developing an algorithm to demonstrate how computers could quickly determine the shortest route between Rotterdam and Groningen. Since then, modified versions of Dijkstra's formulation comprise the processing backbone of systems such as Google Maps and Apple Maps.

Explore what each organelle does within various types of cells

In "Cell Anatomy Viewer," users can explore interactive illustrations of animal, plant, fungal, and bacterial cells. Clicking on an organelle, such as a lysosome, the nucleolus, or the Golgi complex, provides descriptions of its characteristics and functions.

Guess US city populations via bracket-style game

The US Census Bureau's data visualization team created a game—laid out like a March Madness basketball bracket—where you try to decide which metro area of two has the greater population. Test your knowledge of relative city populations and see...

Explore the state of religious freedom worldwide with an interactive data visualization.

Why Google Search's ranking system combines filters, signals, and machine learning layers

Rather than static rankings, dynamic tools continually shift search results in real time. These include Twiddlers, which adjust ranking positions based on document traits and search context, and FreshnessNode, which reshuffles top results to prioritize timely informational content.

Play an incremental game that teaches the history of particle physics

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.

Visualizing the growth of botnets

Botnets are a network of computers that have been infected with a variant of malware that coordinates and leverages them for automated mass attacks such as data theft and crashing servers. This interactive map highlights where botnets have been located between 2014-2020.

Visualizing the consequence of data breaches

To get a sense of the grim state of data security today, take a look at this infographic from TruthFinder that explains why 2018 was the year of the data breach tsunami.

The first algorithmic random number generator was developed in 1946

Although previous methods of randomness involved physical tools with limited outcomes, such as dice, or relied on chaotic variables for number generation, such as electronic noise, John Von Neumann's middle-square method turned the problem into a mathematical computation. It has since been replaced by methods that generate numbers from unique initial values, such as the time on a clock.