Big ideas,
drawn simply.
Friendly, illustrated guides to the mathematics hiding inside nature, patterns, and generative art.
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Read from the beginning, or jump straight to the part that makes you curious.
Golden Angle & Phyllotaxis
Why sunflowers, pinecones, and leaves often arrange themselves around 137.5°—and how one simple rule creates dense, beautiful spirals.
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L-System Production Rules
A practical guide to rewriting symbols into branches, curves, and surprisingly lifelike plants.
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Spiral Types Compared
Fermat, Archimedean, and logarithmic spirals can look alike at first glance. Their spacing tells three very different stories.
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Tiling Symmetry Groups
Every infinitely repeating flat pattern belongs to one of just 17 wallpaper groups. Here is how to spot the transformations.
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Making Reproducible Generative Art
How a seed turns chance into a coordinate you can revisit, share, test, and build upon.
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Pseudo-Random Number Generators
How deterministic machines produce useful unpredictability—and how to choose one for art, simulation, or security.
Read the guide →Fifty more questions
ready to explore.
Every card now opens a full visual lesson with an explainer, a code-drawn diagram, a practical exercise, and a route into the interactive tools.
01Patterns in NatureThe quiet rules that make leaves, shells, clouds, and crystals feel alive.8 guides
Fibonacci Numbers in Living Things
When the famous sequence is useful, and when it is only a tempting coincidence.
Why Leaves Avoid Each Other
How a growing stem distributes leaves for light, rain, and room.
The Geometry of a Pinecone
Read opposing spiral families without having to count every scale.
Shells: Growth, Not Golden Magic
Compare real shells to logarithmic spirals and learn where the model bends.
Honeycomb and the Hexagon
Why six-sided cells use space so efficiently.
Cracks, Veins, and Branching
A visual tour of the branching rules behind rivers, lungs, and lightning.
Snowflakes and Sixfold Symmetry
How water molecules constrain an endless family of icy forms.
Packing Seeds Without Gaps
The Voronoi-like neighborhoods hidden in a sunflower head.
02Shape LanguageA friendly toolkit for symmetry, tiling, ratios, and the geometry of looking.9 guides
Symmetry: The Four Moves
Translation, rotation, reflection, and glide reflection in one visual field guide.
How Tessellations Cover a Plane
Why triangles, squares, and hexagons tile easily—and pentagons are trickier.
The Mathematics of Islamic Geometric Art
Star polygons, grids, and repeated constructions explained respectfully and clearly.
Escher’s Impossible-Looking Tilings
How a repeating grid can become birds, fish, and interlocking worlds.
Regular, Semi-Regular, and Wild Tilings
A quick way to classify a pattern by the polygons meeting at each vertex.
Penrose Tilings and Aperiodic Order
How a pattern can have structure without ever repeating.
Ratios You Can See
Turn 1:1, 4:3, 3:2, 16:9, and 9:16 into instant visual intuition.
The Golden Rectangle, Honestly
What it is, how to construct it, and what it does not prove about design.
Circles, Chords, and Beautiful Arcs
The small pieces of circle geometry behind rosettes and radial patterns.
03Generative SystemsInstructions become images when you give a rule room to repeat.9 guides
The Anatomy of a Generative Sketch
Separate the canvas, palette, rule, randomness, and export into a useful mental model.
Rules, Constraints, and Surprise
Why good generative art needs both freedom and a fence.
A Beginner’s Guide to Noise
What smooth random fields are and why they feel more natural than static.
Cellular Automata: Tiny Rules, Big Worlds
How a grid of on/off cells can grow, stabilize, and disappear.
Reaction-Diffusion Patterns
The chemistry-inspired rules behind spots, stripes, and coral-like textures.
Voronoi Diagrams in Art and Nature
Split a plane by nearest point and discover cells, cracks, and mosaics.
Delaunay Triangulation, Made Visual
The companion structure that connects nearby points without skinny surprises.
Recursion Without Fear
Understand self-similarity by drawing a shape inside itself.
Parameter Sweeps as a Creative Habit
How to make contact sheets that turn trial and error into a visual method.
04Math in MotionFollow a change through time: rotations, waves, curves, and moving points.8 guides
Angles Are Turns, Not Tiny Lines
Build an intuitive sense of degrees, radians, and full rotations.
Radians: The Circle’s Native Language
Why one radian is a length, and why calculus loves it.
Sine Waves, Drawn From a Circle
Watch circular motion project into a wave.
Lissajous Figures and Musical Ratios
How two perpendicular oscillations draw graceful looping paths.
Bézier Curves: The Handle Behind the Curve
See how designers steer smooth paths with a few control points.
The Koch Snowflake and Infinite Perimeter
A shape that gains boundary forever while keeping a finite area.
Random Walks and Wandering Lines
When aimless steps produce clusters, paths, and diffusion.
Brownian Motion as a Drawing Tool
Use microscopic-looking wandering to make delicate paths and textures.
05Numbers You Can SeeMake large ideas tangible with digits, distributions, and visual proofs.8 guides
Pi Is a Circle Story
Meet π as a ratio of circumference to diameter before meeting its digits.
Searching for Yourself in Pi
What a digit search can show, and why it does not make the number magical.
Irrational Numbers: Never Repeating, Still Knowable
A picture-first explanation of √2, π, and φ.
Prime Numbers as a Pattern of Holes
Use a sieve to watch composite numbers fall away.
Modulo: The Clock Arithmetic You Already Know
Remainders turn calendars, colors, and rhythms into loops.
Probability Without the Fog
Learn chance through repeated dots, cards, and simple frequencies.
Histograms Tell Shape Stories
Read clusters, spread, skew, and outliers without pretending a chart is neutral.
The Birthday Paradox, Illustrated
Why shared birthdays become likely faster than intuition expects.
06Creative PracticeSmall, repeatable ways to turn mathematical ideas into personal visual work.8 guides
A Seven-Minute Pattern Warm-Up
A repeatable prompt for making one small pattern before you overthink it.
Build a Palette From One Color
Use hue, saturation, and value rules to make a coherent family.
Composition With a Grid You Can Bend
Treat grids as a starting rhythm rather than a cage.
How to Name a Generative Artwork
A practical metadata recipe for seeds, versions, and exports.
Making a Contact Sheet of Variations
Compare many outcomes at once and learn what your parameters are doing.
From Screen Pattern to Print
Prepare line weight, dimensions, color mode, and resolution for paper.
Make a Generative Zine Page
Combine a rule, a caption, and a small visual sequence into a shareable page.
A Critique Checklist for Algorithmic Art
Ask whether the rule, variation, framing, and finish are all doing their jobs.
See it. Understand it. Play with it.
Start with the picture
Every idea begins with a visual, so you can see the shape before meeting the notation.
Unpack one rule
Short explanations and worked formulas show what creates the pattern.
Change it yourself
Each guide connects to a live tool where the numbers become something you can move.
Keep a question in your pocket.
Curiosity is enough to begin.
Open the playground ↗