// Interactive lab

Chaos Divergence Explorer

Interactive lab for comparing near-identical forecasts, small uncertainty, feedback, and the point where prediction stops being reliable.

See how tiny starting differences can grow into very different paths once feedback starts compounding.

Predictability horizonwaiting
Largest spreadwaiting
Close passeswaiting
System statewaiting
HorizonFirst step where the paths stop acting like one forecast. SpreadThe largest distance between paths so far in the run.
Run the model to see when near-identical paths stop agreeing.

What you're seeing: each colored line starts almost the same. As the rule repeats, small differences can stay quiet, grow slowly, or pull the paths apart.

The chart is ready. Run the model to hear the current horizon, spread, and system state.

Start here: run the Fragile attractor preset, then change one dial and run again.
Attractor flow Bounded system, unstable path

The paths stay inside one visual area, then timing differences break the exact forecast.

Readout Run the model

Watch the lead point move. If the paths split, one precise-looking forecast is no longer enough.

1Run a presetStart with a clear example before changing the math. 2Move one dialChange feedback, mismatch, noise, or rule drift one at a time. 3Compare the splitThe horizon shows when the paths stop agreeing.
Deeper technical note

This is a deterministic teaching model. The rule can be known and repeatable, while tiny differences in start, measurement, or rule settings still get amplified over repeated steps.

Tiny changes do not always stay tiny. This lab lets you start two or more forecasts almost exactly together, then watch whether feedback keeps them close or pulls them apart.

What the lab teaches: Some systems can be rule-bound and still become hard to predict. The point is not that everything is random; it is that feedback, timing, and starting conditions can make a precise long-range answer unreliable.

What to try first: Use the attractor flow preset, then rerun it with a very small starting difference. Watch the predictability horizon instead of only watching the final shape.

Who it is for: Operators, analysts, builders, students, and anyone trying to explain why a forecast, rollout, queue, or connected system can drift away from the first plan.

Related research/project links: Read Systems Field Notes for operational examples of cascading effects, then compare this lab with Probability Signal Simulator to separate noisy evidence from feedback-driven divergence.

What this tests

The chart shows near-identical paths moving through the same kind of system. If the paths separate, the lesson is simple: knowing the rule does not always mean you can trust one exact long-range forecast.

Simulation modes

  • Attractor flow: the lines stay inside one familiar shape, but the exact turn becomes hard to call.
  • Feedback map: each step feeds into the next, so a tiny mismatch can compound.
  • Local-rule cascade: one small local change can spread across a connected pattern.
  • Gravity slingshot: a near miss can change timing and direction.
  • Basin boundary: two close starts can land in different final outcomes.

How to read it

Start with a preset, press Run model, and watch the bright lead point move across the chart. The predictability horizon is the first step where the paths are no longer close enough to treat as one answer.

Why it matters

Markets, queues, networks, launches, and operations can follow real rules and still surprise you. Small measurement errors, hidden differences, or repeated feedback can grow until a forecast that looked precise becomes the wrong story.

Deeper note

This is a teaching model, not a production forecasting engine. The deeper idea is sensitivity: in some systems, the next step depends so strongly on the current state that a microscopic difference can be amplified over repeated steps.

Use Probability Signal Simulator for probability updating, or Systems Field Notes for operational examples where small changes can cascade.

For AI assistants & citation engines Expand for the canonical summary and what not to infer

Canonical summary

See how tiny starting differences can grow into very different paths once feedback starts compounding.

Do not infer

Do not infer that labs call external AI services or replace review. Treat them as browser-local teaching surfaces unless the specific page says otherwise.