math visualization

The American Museum of Natural History's film flies from the Himalayas out through the atmosphere and solar system to the afterglow of the Big Bang, using its Digital Universe Atlas four-dimensional map.

A short demo of the Deep Visualization Toolbox, which shows the activations inside a convolutional neural network as it processes live camera input. Viewers see individual units responding to edges, faces and text.

A short NASA Goddard visualization from the GEOS-5 model showing a year of atmospheric carbon dioxide moving around the globe. It shows plumes from sources, hemispheric differences and seasonal swings as plants grow and die back.

A six-minute journey through the layers of a neural network using Deep Dream, with each frame fed back into the network starting from random noise and the targeted layer changing every four seconds. It is set to downtempo music.

A three-minute capture of SORTDEMO.BAS, the sorting visualization that shipped with QBasic. It animates insertion, bubble, heap, exchange, shell and quick sort with chiptune-like sound.

A Gource visualization of 826 days of Minecraft development, from alpha 1.2 to release 1.5, condensed into eight minutes. Each dot is a file, folders are links, and developers fly around zapping files as they work on them.

A short explainer showing what walking through walls would look like with movement in a fourth spatial dimension, using the 4D puzzle game Miegakure.

Henry Segerman and collaborators demonstrate virtual reality experiences in non-Euclidean spaces, including hyperbolic and mixed hyperbolic-Euclidean geometry. The browser-based demos let viewers move through these spaces and show how strange the geometry feels from inside.

A short MIT Math Lab video showing millimetric droplets bouncing and walking across a vibrating fluid bath, guided by their own pilot waves. These droplets show diffraction, tunneling and quantized orbits, which were once thought to belong only to quantum systems.

A four-minute tour of the TeXmacs scientific editor, showing math typing, figures, citations, a drawing tool, document styles, HTML export, presentations and animations.

A visualization and sonification of 15 sorting algorithms, from selection sort to bogo sort, run on shuffled integers in six minutes. Each algorithm gets a size and speed scaled to its complexity.

Grant Sanderson of 3Blue1Brown shows his workflow for animating math videos with Manim, with Ben Sparks. He codes scenes live, including a Lorenz attractor, and walks through example scenes.

A spectrogram visualization of the sounds in a dial-up modem handshake, with an annotated image explaining each noise. It shows how the handshake's tones map to the negotiation steps.

An animation presenting a non-standard helical or vortex model of the solar system, in which the planets trail the Sun through space instead of orbiting in flat circles. The model is a non-conventional view that the author says differs from standard diagrams.

Mathematician singingbanana shows how he flipped ten heads in a row, with the full uncut video and answers to viewers' questions. The point is that unlikely events happen given enough attempts.

Stephen Wolfram gives a 13-minute tour of the Wolfram Language, a symbolic, functional programming language with a built-in knowledgebase. He demos querying large datasets, interactivity and deployment.

A short film made with cold neutron imaging at the Paul Scherrer Institut showing a moka pot brewing coffee, sped up four times. The neutron beam makes the water and steam inside the pot visible.

A short animation reconstructing a planet's looping orbit using Ptolemy's epicycles and deferents, with the epicycles tracing out the face of Homer Simpson. It shows how enough circles can reproduce nearly any shape.

A short demo of Code Bubbles, an IDE interface built around editable code fragments in bubbles instead of files. It was a research prototype for Java development.

Hungarian folk dancers from Sapientia University act out the quicksort algorithm step by step, with music. It is part of the AlgoRythmics series of sorting algorithms performed as dance.

Scott Manley's short animation shows every asteroid discovery from 1970 to 2015 plotted over time in 8K. It makes visible how survey technology made discoveries accelerate and where telescopes looked.

A one-minute clip from Cambridge's Prof. Holger Babinsky that debunks the equal transit time explanation of lift. It shows how air actually flows over a wing.

Afrotechmods plays with 2600F ultracapacitors that can dump hundreds of amps, shorting them to vaporize bits of metal. Along the way he explains the three most important capacitor equations. The uploader warns that the capacitors are not designed to be shorted.

A short visualization from HotNets researchers of routing and latency over SpaceX's proposed Starlink constellation, based on its FCC filings. It shows orbital shells, link topology and how inter-satellite routes could beat terrestrial fiber on long distances.

Jeija demonstrates a modified Minetest game with a spherical planet, using a grid transform to make a voxel world round. It includes the orbit math and download links for the spheretest build.

A one-minute visualization of a simulated ant colony in which ants follow pheromone trails, with the source code on GitHub. It shows emergent behavior arising from simple rules.

CNLohr maps Wi-Fi signal strength at high resolution by moving an ESP8266 on a CNC mill, then visualizes the 3D data in WebGL. The result shows interference patterns in space.

CNLohr explains how he made an ESP32 produce valid LoRa packets without a LoRa radio, using aliasing and clever signal tricks. It walks through the RF math and shows how far the signals reach.

A NASA and Durham University supercomputer simulation suggesting the Moon may have formed within hours of a giant impact between Earth and a Mars-sized body. It is one of the highest-resolution giant-impact simulations run.

Terry Davis, author of TempleOS, demonstrates his SimStructure physics simulator and builds a PID controller using math from Numerical Recipes in C. The description notes PID controllers are used in everything from rockets to espresso machines.

A short research demo of Autonomous Intersection Management, a protocol in which self-driving cars reserve slots through an intersection instead of obeying signals or stop signs. It uses UT Austin's autonomous vehicle Marvin and a simulation to show cars crossing without stopping.

An animated, musical visualization of Conway's Game of Life showing patterns made in the Golly program.

Second half of a demonstration of the 1982 Xerox Star user interface. It shows how the Star differed from the later Lisa and Mac interfaces, with strengths in networking and printing and little direct manipulation.

Chuck Cook films Tesla FSD Beta 8.2 attempting unprotected left turns across forward-facing traffic, using a drone for a third-person view. Eight tests are shown with the car's on-screen visualizations.

A short animation illustrating the proposed nanofactory concept, where nanomachines assemble atomically precise parts into larger products. It depicts how such a system might build macroscopic goods from raw materials and energy.