Feedback and Cascades
Systems where an event makes the next event more likely: self-organized criticality, self-excitation, herding, forced selling, and the multiplier on flow.
Nine simulations of the same underlying shape: a system where the occurrence of one event changes the probability of the next. When that coupling is weak, disturbances die out and averages describe the system well. As it approaches one, the same small disturbance can produce a response of any size, and the average stops being a useful summary. Nothing here is fitted to market data — each demo generates its own from parameters you set.
Sandpile avalanches
Can a system arrive at the edge of instability without anyone tuning it there?
Try this. Drop grains steadily and leave it running while the histogram fills. No parameter sets the distribution of avalanche sizes; the pile finds its own slope and then stays there, releasing through slides of every scale.
Assumptions and limits. The Bak–Tang–Wiesenfeld pile has one toppling rule and no agents, prices, or money. It demonstrates that scale-free avalanches can be self-organized rather than tuned. It is not evidence that any particular market is a sandpile.
Essay: Sandpiles and Crashes · Source
Branching ratio
Why does “just below one” behave so differently from “just above”?
Try this. Compare 0.95 and 1.05. The parameter moves by a tenth; the qualitative behaviour changes completely. Then sit at 0.99 and watch how long a single spark can keep going.
Assumptions and limits. A branching process assumes each event independently spawns offspring with a fixed mean. Real cascades happen in finite systems with correlated offspring and exhaustible fuel, all of which cut the tail short.
Essay: Life as a Double Fixed Point · Source
Self-exciting events
When does one event start a family of events?
Try this. Start at a branching ratio of 0.3, where the intensity curve returns to baseline between events. Push it toward 1 and watch it stop coming back down: the cluster sustains itself long after the original outside event.
Assumptions and limits. The parameters are set by hand, not estimated from any market. A branching ratio near one is a property of this generator, not a measurement of anything real.
Essay: Reflexivity by the Numbers · Source
Herding on a lattice
Does a large move require a cause proportional to its size?
Try this. Hold news at zero, so there is no external information at all, and raise copying past the critical temperature. The grid still commits to a side. Then sit just below the critical point and watch clusters of every size form.
Assumptions and limits. A lattice of imitating spins is not a market. It shows that collective swings can emerge from local copying with no news; it says nothing about which real episodes were of this kind.
Essay: Crashes Without a Cause · Source
Reflexive feedback
What happens when beliefs move prices and prices move beliefs?
Try this. Give the system one shock at low feedback and watch it decay. Repeat the identical shock at high feedback: the same input now leaves a swing that outlives it.
Assumptions and limits. Two coupled variables, no explicit agents and no trading mechanics. It is a picture of the loop Soros described, not a model of how any market implements it.
Essay: Markets as Reflexive Fixed Points · Source
Volatility clustering
Why does volatility arrive in bursts rather than evenly?
Try this. Set memory to nearly zero for a baseline of independent jumps, then raise it. The shocks are drawn the same way throughout; only the memory changes, and the calm and violent stretches appear.
Assumptions and limits. This is a GARCH-flavoured generator: it produces clustering by construction. That demonstrates the mechanism is sufficient to produce the pattern, not that it is the mechanism operating in real returns.
Essay: Markets as Reflexive Fixed Points · Source
Risk models creating risk
What happens when everyone measures risk the same way?
Try this. Increase the number of balance sheets following the same rule. The initial shock stays the same size; the response does not.
Assumptions and limits. One rule, one asset, and no variation in funding, horizon, or willingness to buy. A sketch of the mechanism behind a deleveraging spiral rather than a model of one.
Essay: When Risk Models Create Risk · Source
Leverage cascade
Why do losses accelerate instead of arriving at a steady rate?
Try this. Fix the shock and raise leverage alone. Then restore leverage and cut liquidity instead. Both routes reach forced selling, which is the point: the fragility is in the combination, not in either number.
Assumptions and limits. Purely mechanical. No central bank, no buyers stepping in at a discount, no differences between holders. Real cascades stop for reasons this model has no way to represent.
Essay: Markets as Reflexive Fixed Points · Source
Inelastic markets
How much does it actually cost to move a market?
Try this. Send the same flow into both settings. The gap between the two lines is the multiplier, and it is the whole argument: under the deep-market intuition that flow is nearly free, the red gap should not exist.
Assumptions and limits. The multiplier is a dial here, not an estimate. Gabaix and Koijen put it around five for US equities; this demo lets you set it to whatever you like, which makes it a way to build intuition rather than evidence for any particular value.