# Graph Paper

> Graph Paper is a graphing notebook for visual thinking. Plot functions, explore equations, and visualize data in your browser.

For AI agents and programs:

- Instructions: https://graph-paper.io/for-agents/en/index.md
- Make a link: POST https://graph-paper.io/plot-link with the JSON plot document as the body (or GET https://graph-paper.io/plot-link?doc=<percent-encoded JSON>); the answer has the link, or the errors.
- MCP server: https://graph-paper.io/mcp (Streamable HTTP, no authentication; MCP Registry name io.graph-paper/graph-paper; server card https://graph-paper.io/mcp/server-card).
- In-browser tools for a signed-in person: https://graph-paper.io/agent-tools.json

## Capabilities
- 2D plots: functions, parametric and polar curves, implicit curves and regions, heatmaps with contour lines, vector fields, complex domain coloring, points and polygons; annotations (labels, segments with arrows, rules, bands) as markers that the person can move.
- 3D plots: surfaces, parametric surfaces and curves, implicit surfaces, point sets, spheres, segments and arrows.
- Interaction: sliders, animation, draggable points, and actions that change values once or on a timer.
- Data: tables, scatter plots, bar charts, histograms, box plots, candlestick charts, and fits of a formula to data.
- Notebooks: documents that mix prose, formulas, computations and figures.
- Sharing: public links, shared folders, collaborators and real-time editing.
- Hand a plot to a person: https://graph-paper.io/new#doc=<base64url of the JSON document>, or https://graph-paper.io/new#json=<percent-encoded JSON>, opens it as an editable draft; the format is at https://graph-paper.io/plot-document-format/en/.
- Check a plot document and get its link: POST https://graph-paper.io/plot-link with the JSON document as the body (or GET https://graph-paper.io/plot-link?doc=<percent-encoded JSON>). No account and no key. OpenAPI description: https://graph-paper.io/openapi.json.
- MCP server: https://graph-paper.io/mcp (Streamable HTTP, no authentication), with the tools make_plot_link, get_plot_format and list_examples.
- No HTTP API reads or writes a person's private documents, and there are no API keys; public documents can be read. A signed-in person can allow in-browser tools (see agent-tools.json).

## Main
- [Graph Paper](https://graph-paper.io/): Plot functions, explore equations, and visualize data in the browser.
- [Showcase](https://graph-paper.io/showcase/en/): Gallery of example graphs and visualizations.
- [Tips and Tricks](https://graph-paper.io/tips-and-tricks/en/): Tips and tricks for getting the most out of Graph Paper.
- [Plotting Guide](https://graph-paper.io/plotting-guide/en/): Lists, points, restrictions, colors, and a Desmos translation table for building complex plots in Graph Paper.
- [For Agents](https://graph-paper.io/for-agents/en/): For programs and AI agents: what Graph Paper can draw, how to open a plot for a person with a link, and what can be read without an account.
- [Plot Document Format](https://graph-paper.io/plot-document-format/en/): The JSON format of a Graph Paper plot document: every field, every series type, and complete examples with links that open them.
- [Documentation](https://graph-paper.io/docs/en/): The documentation of Graph Paper: guides for people, pages for programs and AI agents, and file formats. No account is needed to read it.
- [Full text](https://graph-paper.io/llms-full.txt): The complete English text of For Agents, Plot Document Format, Plotting Guide and Tips and Tricks, in one file.

## Showcase
- [Mandelbrot Set](https://graph-paper.io/showcase/en/mandelbrot-set): The classic fractal defined by iterating complex quadratic polynomials.
- [Julia Set](https://graph-paper.io/showcase/en/julia-set): Iterating z² + c with the constant c animating around a circle, sweeping the whole family of Julia fractals.
- [Rainbow Trigonometry](https://graph-paper.io/showcase/en/rainbow-trig): Six offset sinusoids.
- [Polar Roses](https://graph-paper.io/showcase/en/polar-roses): A polar rose r = sin(kθ) whose petal count steps as the integer k animates through a discrete set.
- [Damped Oscillation](https://graph-paper.io/showcase/en/damped-oscillation): A decaying sinusoid whose damping coefficient animates — the exponential envelope tightens and loosens as c sweeps.
- [Domain Coloring](https://graph-paper.io/showcase/en/domain-coloring): A complex power z^a whose exponent animates, winding the phase more times around the origin.
- [Wave Interference](https://graph-paper.io/showcase/en/wave-interference): Two point sources create ridges of constructive and destructive interference.
- [Spherical Harmonics](https://graph-paper.io/showcase/en/spherical-harmonics): The angular shape of atomic orbitals — four lobes of a d-orbital.
- [Implicit Heart](https://graph-paper.io/showcase/en/implicit-heart): A classic heart shape defined by the zero set of an algebraic equation.
- [Contour Landscape](https://graph-paper.io/showcase/en/contour-landscape): Elevation lines of a surface with two peaks and a saddle point.
- [Möbius Strip](https://graph-paper.io/showcase/en/mobius-strip): A surface with only one side — follow the edge and you return flipped.
- [Spiral Galaxy](https://graph-paper.io/showcase/en/spiral-galaxy): Logarithmic spirals winding outward — the blueprint of spiral galaxies.
- [Saddle Surface](https://graph-paper.io/showcase/en/saddle-surface): A hyperbolic paraboloid — curves up in one direction and down in the other.
- [Butterfly Curve](https://graph-paper.io/showcase/en/butterfly-curve): A delicate parametric curve discovered by Temple Fay.
- [Lissajous Family](https://graph-paper.io/showcase/en/lissajous-family): A 3:2 Lissajous curve whose phase offset animates, braiding through the whole one-parameter family.
- [Conchoid of Sluze](https://graph-paper.io/showcase/en/conchoid-of-sluze): An implicit algebraic curve with a cusp and asymptote at x = 1.
- [Superellipse Family](https://graph-paper.io/showcase/en/superellipse-family): An implicit superellipse |x|^n + |y|^n = 1 whose exponent animates, morphing from astroid through circle to squircle.
- [Fourier Harmonics](https://graph-paper.io/showcase/en/fourier-harmonics): A composite wave with its individual harmonic components shown separately.
- [Implicit Bouquet](https://graph-paper.io/showcase/en/implicit-bouquet): Folium of Descartes, Bernoulli lemniscate, and astroid composed in one implicit plot.
- [Buck-Boost Converter](https://graph-paper.io/showcase/en/buck-boost-converter): Normalized input resistance vs. duty ratio for buck, boost, and buck-boost DC-DC converters.
- [Kernel Functions](https://graph-paper.io/showcase/en/kernel-functions): Common kernels for density estimation: Gaussian, Epanechnikov, quartic, tricube, and uniform.
- [Klein Bottle](https://graph-paper.io/showcase/en/klein-bottle): A non-orientable surface that passes through itself in 3D — a bottle with no inside.
- [Boy's Surface](https://graph-paper.io/showcase/en/boys-surface): An immersion of the projective plane — a one-sided surface with three-fold symmetry and a single triple point.
- [Roman Surface](https://graph-paper.io/showcase/en/roman-surface): Jakob Steiner's quartic model of the projective plane — four lobes with tetrahedral symmetry meeting at a triple point.
- [Cross-Cap](https://graph-paper.io/showcase/en/cross-cap): The simplest self-intersecting model of the projective plane — a pinched cap with one double-point segment and two pinch points.
- [Trefoil Knot](https://graph-paper.io/showcase/en/trefoil-knot): The simplest non-trivial knot — a closed curve that cannot be untied without cutting.
- [Seashell](https://graph-paper.io/showcase/en/seashell): A logarithmic spiral shell — nature’s own parametric surface.
- [Double Helix](https://graph-paper.io/showcase/en/double-helix): Two intertwined helices joined by rungs — the iconic shape of DNA.
- [Torus Knot Family](https://graph-paper.io/showcase/en/torus-knot-family): Three torus knots at different winding ratios stacked in one scene.
- [Frenet Frame](https://graph-paper.io/showcase/en/frenet-frame): Tangent, normal, and binormal vectors riding along a space curve.
- [Iris Species](https://graph-paper.io/showcase/en/iris-clusters): Sepal length vs. petal length for three iris species — Fisher's classic clustering dataset.
- [Hertzsprung–Russell Diagram](https://graph-paper.io/showcase/en/hr-diagram): Stellar luminosity vs. surface temperature, with main sequence, red giants, and white dwarfs.
- [Geyser Eruptions](https://graph-paper.io/showcase/en/geyser-eruptions): Eruption duration vs. waiting time, modeled on the bimodal pattern of Old Faithful.
- [Normal Distribution](https://graph-paper.io/showcase/en/normal-density): A density-normalized histogram of a Gaussian sample, with the analytic bell curve overlaid.
- [Bimodal Wait Times](https://graph-paper.io/showcase/en/geyser-wait-times): Geyser waiting times showing a clear bimodal distribution, modeled on Old Faithful.
- [Monthly Rainfall](https://graph-paper.io/showcase/en/monthly-rainfall): Average monthly precipitation in a temperate maritime climate, modeled on Seattle.
- [Exam Scores by Section](https://graph-paper.io/showcase/en/exam-scores-by-section): Distribution of exam scores across four lab sections, showing medians, quartiles, and outliers.
- [Sample Price Series](https://graph-paper.io/showcase/en/tych-stock-series): Open-high-low-close data for fictional ticker TYCH over 30 trading days, showing a breakout from consolidation.
- [Limaçon Family](https://graph-paper.io/showcase/en/limacon-family): An animated polar limaçon r = a + cos(θ) whose offset a sweeps through the inner-loop, cardioid, and dimpled forms.
- [Electric Dipole](https://graph-paper.io/showcase/en/dipole-field): The vector field of a 2D electric dipole, with field lines flowing from positive to negative charge.
- [Gaussian Width](https://graph-paper.io/showcase/en/gaussian-explorer): The normal density bell with an animated standard deviation — it widens and flattens as the spread grows, and spikes as it shrinks.
- [Lagrange Points](https://graph-paper.io/showcase/en/lagrange-points): The five points where a satellite can hold still relative to the Sun and Earth — found where two force-component curves cross — with the Earth mass animating.
- [Plasma Effect](https://graph-paper.io/showcase/en/plasma-effect): A drifting plasma pattern: two waves multiplied into one scalar field, shaded by a cosine ramp, with time animating.
- [Creation](https://graph-paper.io/showcase/en/creation-shader): A classic demoscene shader: a unit grid pushed outward by a breathing ring wave, read as a glowing distance field, with time animating.
- [CIE Chromaticity Diagram](https://graph-paper.io/showcase/en/cie-chromaticity): The horseshoe of all visible colors, each point painted with the sRGB color of its chromaticity by a color formula, with the sRGB gamut triangle inside it.
- [Game of Life](https://graph-paper.io/showcase/en/game-of-life): Conway's Game of Life running live: a 150 × 150 board stored as one list, stepped ten times a second by an action, drawn as a heatmap.
- [Exoplanet Transit](https://graph-paper.io/showcase/en/exoplanet-transit): A planet crossing its limb-darkened star, with the light curve an observer would record: a flat-bottomed dip for a uniform disc, a rounded, deeper one for the real star.
- [Trigonometric Tapestry](https://graph-paper.io/showcase/en/complex-trig-sum): Six nested trigonometric functions, each turned by a sixth root of unity, summed and painted over the complex plane.
- [Voronoi Diagram](https://graph-paper.io/showcase/en/voronoi-diagram): Sixteen drifting sites split the plane into colored cells: every point takes the color of its nearest site, with time animating.
- [Rainbow Refraction](https://graph-paper.io/showcase/en/rainbow-refraction): One ray of white light through a water droplet: refracted in, reflected once, refracted out, and split into a fan of colors, with the impact height animating.
- [Metaballs](https://graph-paper.io/showcase/en/metaballs): Ten soft blobs that drift, merge and split again, with time animating.
- [Knotted Tube](https://graph-paper.io/showcase/en/frenet-knot-tube): A rainbow tube around the (3, 5) torus knot, built on its Frenet frame.
- [Poly Banana](https://graph-paper.io/showcase/en/poly-banana): A low-poly banana made of 63 flat triangles — an image that only exists from one direction.
- [Platonic Solids](https://graph-paper.io/showcase/en/platonic-solids): The five regular convex polyhedra, side by side, each built from a vertex list and a face table.
- [Three-Body Problem](https://graph-paper.io/showcase/en/three-body-problem): Three equal masses under Newton's gravity, stepped live by an action: the figure-eight orbit, and an equilateral triangle that turns and then breaks up into chaos.
- [Lorenz Attractor](https://graph-paper.io/showcase/en/lorenz-attractor): Edward Lorenz's model of convection, integrated live in 3D: the orbit never repeats, yet it stays on a butterfly-shaped attractor.
- [Kelvin Wake](https://graph-paper.io/showcase/en/kelvin-wake): The V-shaped wave pattern behind a ship in deep water: its wavelength changes with the ship's speed, but its half-angle stays 19.47°.
- [Underwater Caustics](https://graph-paper.io/showcase/en/underwater-caustics): Sunlight refracted by a wavy water surface gathers into moving bright lines: the patterns on the floor of a swimming pool.
- [Vibrating Drum](https://graph-paper.io/showcase/en/vibrating-drum): A circular drumhead with a fixed rim, vibrating in three normal modes at once: Bessel functions in motion.
- [Joukowsky Airfoil](https://graph-paper.io/showcase/en/joukowsky-airfoil): Air flowing past a wing, found by mapping the flow around a circle with Z = z + 1/z; the angle of attack animates.
- [Greek Wave Frieze](https://graph-paper.io/showcase/en/greek-wave-frieze): The running wave of Greek pottery, drawn by one formula and wound into a spiral mosaic; the band slides along itself without end.
- [Gyroid](https://graph-paper.io/showcase/en/gyroid): Schoen's gyroid, the minimal surface that divides space into two intertwined labyrinths, approximated by the level set of sin x cos y + sin y cos z + sin z cos x; the level animates.
- [Apollonian Gasket](https://graph-paper.io/showcase/en/apollonian-gasket): Circles packed inside a circle without end, each new one touching three others; Descartes' theorem gives its size, and every curvature is a whole number.
- [Spirograph](https://graph-paper.io/showcase/en/spirograph): A wheel rolling inside a ring, with a pen that traces a hypotrochoid; the wheel animates, and the sizes of the ring and wheel and the pen's distance from the wheel's centre can be edited.
- [Whirling Squares](https://graph-paper.io/showcase/en/whirling-squares): Squares nested in a square, each one turned and shrunk by the same step, so their corners run along four spirals; the step animates.
- [Projectile with Air Drag](https://graph-paper.io/showcase/en/projectile-with-drag): A ball thrown through air, computed step by step with a drag force that grows as the square of the speed, beside the parabola it would follow without air.
- [Predators and Prey](https://graph-paper.io/showcase/en/predator-prey): The Lotka–Volterra model in the plane of the two populations: a direction field, the closed orbit of a solution, and a state that an action moves around it.
- [Adding Points on an Elliptic Curve](https://graph-paper.io/showcase/en/elliptic-curve-group-law): The chord construction on the curve y² = x³ − 2x + 1: the line through two points meets the curve in a third point, and its mirror image is their sum.

## Legal
- [Privacy Policy](https://graph-paper.io/privacy-policy)
- [Terms of Service](https://graph-paper.io/terms-of-service)