The bench, after hours.

The Cartographer

Four discovery policies, the same hidden business, and a fixed learning budget. Compare top-five recovery across paired simulations; inspect the proxy error, uncertainty, and assumptions behind every result.

Thirty possible growth levers. Five worth finding. How much should you learn cheaply before putting an experiment in front of customers? Map the terrain, then reveal what each strategy missed.

Four maps of a country nobody has seen. One follows the largest landmark; one reads the old surveys; one asks an imperfect guide; one decides which question to ask next. Lift the fog.

The Allocator

Three real strategies spend identical traffic on one seeded, noisy market: sequential fixed-horizon A/B testing, Thompson-sampling bandits, and auto-research that measures which lever matters before optimizing any of them. The dashed line is the market's true ceiling; the gaps below it are regret.

The argument for AI-native growth, run as a race. The quarterly cadence was built for few levers and big effects — drag the era dial toward today (many, small, drifting) and watch it fall behind machines that reallocate every visitor. Note what auto-research does first: it finds the highest-order bit.

Three gamblers, one table, the same deck. One bets by the quarter, one by the hand; one asks first which game is worth playing. The house keeps what hesitation leaves.

Suminagashi, Surveyed

A real-time fluid simulation — the “stable fluids” method games and film use — rendered not as ink but as a live topographic survey: contour lines, slope hachures, pressure isobars that appear only where the water actually moves.

Markets move like water: you never see the flow, only what it did. This is instrumentation's whole job — the invisible current, made legible while it's still moving. Touch the water and watch the map react.

Real fluid dynamics read as a survey: the marbling tray's flow rendered as hillshaded terrain — contour lines, iron-filing hachures down the slopes, ember pressure isobars only while the water moves. Stable fluids in raw WebGL2.

Strange Loop

A camera pointed at its own picture: each frame is rotated, scaled, and fed back in until the image becomes a stable fixed point — a picture made entirely of itself. The endless zoom is the visual form of an ever-rising canon.

This is what a growth loop literally is: output fed back as input. Content brings users; users make content. The image that stabilizes is the steady state every compounding loop converges to — design the transform and the result draws itself.

After GEB: a specimen frame holding a live picture of itself — real video feedback, the image as the fixed point of its own transform. The zoom is a canon per tonos: descend forever, arrive where you began. Drag sideways to twist the hierarchy.

Criticality

A branching process: every ember spawns a random number of children averaging k. The math allows no middle — below one, every cascade dies; above one, it never stops. Epidemiologists call the same number R₀.

The viral coefficient, made physical. Every referral program lives on this knife: invites-that-convert per user below 1 and the campaign fades no matter how big the launch; above 1 and it runs away. Drag k a hair either side and feel how narrow “word of mouth” really is.

The viral coefficient as weather: an ember cascade where every spark's fate hangs on k. Below one, every fire dies; above one, every fire eats the tray — and there is no stable middle. Drag to move k; feel the knife edge.

Morphogenesis

Turing's 1952 model of pattern formation: two chemicals — one promoting growth, one suppressing it — diffusing at different speeds produce spots, stripes, mazes, dividing cells. No blueprint anywhere.

Simple local rules, global structure: how communities self-organize and how niches form in markets nobody segmented. You don't design the pattern — you set the conditions and it grows. The ember front shows where growth is happening right now.

Turing 1952: two chemicals arguing produce coral, worms, mazes, mitosing cells — pattern without a patterner — grown live and rendered as a surveyed landform. Paint to seed; cycle the species; the ember front marks where growth is actually happening.

Lenia

A continuous cellular automaton: one growth rule applied everywhere, every frame. A few rare configurations of matter hold together, swim, and heal; almost everything else dissolves. The swimming is not programmed — it survives.

Product-market fit as physics. The space of things you could build is enormous; the configurations that self-sustain are tiny islands in it. Smear matter and watch it dissolve — then watch the one tuned creature glide. Most ideas are smudges.

Continuous cellular automata: soft-bodied creatures that glide, collide, heal, and die — and nobody programmed the swimming. One growth formula, one still portrait of one creature; the rest emerges. Tap to seed, drag to smear matter.

The Loss Landscape

Three real optimization algorithms — SGD, Momentum, Adam — descending an actual loss surface by gradient, live, each leaving the trail its strategy produces. Lower is better; none of them can see the whole map.

Every testing program is one of these hikers: you only ever see the slope where you stand. Jittery small steps, committed momentum, adaptive pacing — and the local minimum that feels like the summit. Drag to raise ground mid-race; markets move under your feet.

Gradient descent as a place: three real optimizers — jittery SGD, overshooting Momentum, adaptive Adam — descend a surveyed mountain, leaving trails. Tap to re-drop them; drag to raise ground under their feet mid-race.

The Boundary

A small, real neural network — 337 weights, training live in the page — that starts believing a straight line separates two spirals and slowly bends its belief around the data. Backpropagation you can watch; nothing pre-trained.

How every model you now work with learns: wrong at first, reorganized by contradiction. Targeting, ranking, segmentation — all boundaries bending around examples. Tap to plant a point it can't explain; the fastest lesson in why data quality is strategy.

A real neural network — 337 parameters, trained live in front of you — whose belief starts as a useless line and slowly wraps itself around the truth. Tap to plant a point it can't explain, and watch it reorganize.

This Page, Measured

A page instrumented like a product: session time, scroll depth, returns — computed on your device, from your reading, shown to you. n = 1, nothing transmitted.

Your own retention curve, session length, and resurrection rate — the metrics I watch for products, pointed at a single reader: you. Every number here is real, which is the whole standard a dashboard should meet.

The strange loop of instrumentation: a page whose only subject is you reading it — your retention curve, your compounding attention, the observer effect live. Every number real, n = 1, nothing leaves your device.

The Tesseract Room

The n-cube family: sweep a point into a segment, the segment into a square, the square into a cube — then the same move once more, along a fourth axis at right angles to all three. What renders is that object's shadow, cast into a room that can't contain it.

Adding a dimension changes what's reachable — a new channel, a new lever, a new axis in the strategy. Everything you already knew is still there; it's just a slice now. Drag through the planes you can't point at: practice for thinking in more variables than you can see.

The n-cube genealogy, drivable: sweep a point to a segment, a square, a cube — and once more along an axis this room doesn't own. Drag to rotate in planes you can't point at; the inner cube isn't inside, it's just farther in w.

Depth, Instead of Height

Scroll position is mapped to a camera moving along a 3D path instead of down a page — the site's red thread rebuilt as geometry you travel through. Raw WebGL2, one file, no libraries.

The same content, experienced as a journey instead of a scroll. For anyone who builds landing pages or product tours: progress people can feel beats length they can measure.

The site's vermillion thread, traveled from inside — scroll drives a camera down a line in space. After the WLT depth-scroll; raw WebGL2, one file, no libraries.