visual math

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

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 clip of Bill Gates demonstrating Visual Basic in 1991, showing drag-and-drop building of a Windows GUI.

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.

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.

Saqib Shaikh, a blind developer, shows how he writes and debugs code in Visual Studio 2017 using a screen reader. The short demo shows an expert doing ordinary developer tasks.

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 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.

Saqib Shaikh, a blind developer at Microsoft, shows at Build 2017 how he writes and debugs code in Visual Studio using a screen reader. This version adds subtitles.

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 two-minute video of Conway's Game of Life running inside Conway's Game of Life, built from OTCA metapixels and Golly. It zooms smoothly between scales.

Tim Hutton's demonstration of SmoothLifeL, a continuous version of Conway's Game of Life using floating point values. It shows gliders traveling in any direction, rotating pairs, and elastic cord-like structures, with config details to run it yourself.

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.

MIT researchers show that sound can be recovered from silent video by analyzing tiny vibrations in objects such as a potato chip bag. It works even with consumer cameras by using rolling shutter.

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.

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

A short Dyalog demonstration building Conway's Game of Life in a single line of APL, step by step. It shows how array operations replace loops.

A Mandelbrot set zoom animation reaching a magnification of about 2.1x10^275, claimed as the deepest at the time (January 2010). Each frame was rendered separately over six months on 12 CPU cores.

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.

An overview of the PTVS 2.0 beta feature for debugging Python and C/C++ together in one session in Visual Studio.

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.

A 12-minute demo of the Alternate Reality Kit, built by Randall Smith at Xerox PARC in 1986. It is a simulated physical world in which users manipulate objects and program by direct interaction.

MIT Media Lab shows an imaging system capturing a trillion frames per second, fast enough to film light pulses travelling through objects in slow motion.

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.

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.

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.

Stargate Studios' 2009 virtual backlot reel shows before-and-after shots in which green screen and compositing replace locations in ordinary TV dramas and comedies. It shows how much of a seemingly real show is computer generated.

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.

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.

Alan Kay demonstrates GRaIL, a graphical input language system from around 1968 in which hand-drawn strokes become boxes, connections and dataflow-style programs.

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.

Jack Gallant's lab demonstrates reconstructing movie trailer clips a subject watched from fMRI brain activity, using regression models trained on hours of viewing data. The video shows the original clip beside the reconstruction.

Deepfake artist Shamook's improved version of the Luke Skywalker scene from The Mandalorian season 2 finale, replacing the official CGI face with a deepfake.

A game-dev video demonstrating a noise shader in Godot where shapes are visible only in motion against animated noise and vanish when the game is paused or screenshotted. The demo is available on GitHub.