The bench, after hours.

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.