The mathematics of shape, number and structure that work can be built on.
A mathematics channel that explains linear algebra, calculus, number theory, neural networks and more through animation. Its way of building understanding through moving diagrams is a model for turning mathematics into film.
The official site of a Japanese composer and artist who works with sound and data. It organises his large-scale audiovisual installations such as datamatics and supersymmetry, his concerts and his recordings by series. A leading example of making numbers and data themselves into the work.
The International Society for the Arts, Sciences and Technology, publisher of Leonardo, the journal founded by Frank Malina in 1968. It is a long-standing home for research and criticism at the intersection of art and science.
A non-profit devoted to the connections between mathematics and art, music, architecture and culture. It runs the annual Bridges conference, held since 1998 and a central venue for mathematical art exhibitions and papers.
The site of a Japanese artist known for the "Star Cage". It presents bamboo sculptures, benches, an origami turbine and other works based on Fibonacci numbers and quasicrystal geometry, along with papers and Fibonacci-based music. The site design is old-fashioned, but it is still being updated.
A personal site collecting algorithm experiments and visual toys. Fractals, reaction–diffusion, chaos, the n-body problem, boids, the travelling salesman problem, Voronoi diagrams and more can be set in motion and explored in the browser.
The site of a mathematical film in nine chapters, about two hours of computer animation that leads from two dimensions to four, and on to complex numbers and fibrations. It can be watched online in many languages, including Japanese, and has a follow-up film, Chaos. A model for putting higher dimensions and complex numbers on screen.
An article listing signed distance functions for primitives such as spheres, boxes and tori, along with operations like union, subtraction, intersection and smooth blending — all with GLSL code. A reference dictionary for building solids from equations.
An interactive piece that redraws any closed shape — a freehand drawing, an uploaded image, or the outline of a country or city — with a chain of spinning circles. You can change the number of circles to see how the approximation improves, and display the spectrum of circle sizes and the breakdown into sine waves in x and y. Circles riding on circles is the same idea that drives spirograph curves.
The hub page of a mathematician working in geometry and topology. It links to 3D-printed sculptures that cast shadows of four-dimensional objects, hyperbolic-space VR, material for the book Visualizing Mathematics with 3D Printing, mathematical dice and more.
The home of a program for drawing mathematical knots and links in three and four dimensions and reshaping them interactively, with a gallery of images made with it. Available for Windows, macOS and Linux — a tool for treating knots as closed curves to shape.
The personal page of a mathematical engineer known for "impossible objects" and ambiguous objects that change shape in a mirror, such as the "ambiguous garage roof". An entry point into designing illusions from mathematics.
A huge archive of mathematical and physical simulation images by a researcher at École polytechnique in France, with more than ten thousand pictures and animations grouped by theme — real numbers, fractals, quantum physics, astronomy and more. The site is old-fashioned and easy to get lost in, but it is still being updated.
A channel in which a mathematician presents famous problems and theorems in number theory and geometry, with a focus on visual proofs. Its many ways of showing properties of numbers as shapes are a good source of ideas for number-themed work.
A collection of musical toys to play in the browser. Musical Spirograph turns a spirograph into musical patterns; others include pendulum waves, Polyrhythm with its polygons, Cellular Sequencer built on the Game of Life, and Wave Drawer for drawing a waveform and hearing it — many let you see and hear a mathematical mechanism at work.
A page extending the classic Ulam and Sacks prime spirals so that each number is drawn according to how many distinct prime factors it has. Every image comes with the Python script that produced it, so you can reproduce and modify them yourself.
A mathematics channel in which mathematicians and researchers each take up one topic about numbers. Number theory — primes, sequences, curious properties of numbers — is especially well covered, explained with hand-drawn diagrams. A good source of ideas for work built on numbers.
A site that walks through "number spirals" — integers wound so the perfect squares line up — and shows, chapter by chapter, the curves that primes and factors trace. The program used for the graphics can be downloaded, making it a good starting point for anyone building imagery from primes.
A creative-coding channel built around p5.js and similar tools. Its "Coding Challenges" build small pieces on fractals, prime spirals, physics simulations and other mathematical and natural phenomena from scratch, on camera. By the same author as The Nature of Code.
An artist who turns mathematical forms into sculpture through metal 3D printing. Known for pieces based on minimal surfaces and polyhedra, as well as laser-etched glass crystals of molecules and proteins.
A sculptor and mathematician working mainly with polyhedra. Alongside his sculptures, the site hosts long-standing educational material such as the Virtual Polyhedra encyclopedia.
Articles on computer graphics, mathematics, shaders and fractals. Its explanations of signed distance functions and raymarching are standard references for anyone drawing shapes with equations.
A studio that designs products and artworks with simulations inspired by natural processes. Founded in 2007 by Jessica Rosenkrantz and Jesse Louis-Rosenberg, it makes 3D-printed jewelry, jigsaw puzzles and more.
A personal site with a vast collection of notes and examples on geometry, fractals, curves and surfaces, visualisation and dome projection. Equations sit alongside code, making it a long-standing reference for makers.
A flexible software sketchbook and language for learning to code within the visual arts. Started in 2001 by Casey Reas and Ben Fry and now stewarded by the Processing Foundation, it remains a classic entry point to generative art.
A book by Daniel Shiffman on simulating natural systems with code. It covers physics, particles, autonomous agents, cellular automata, fractals and genetic algorithms with p5.js, and is freely readable online.
A generative artist who uses algorithms to create painterly work. Besides the work itself, the site publishes essays explaining techniques such as flow fields.