Attractlets
The null case, on purpose: order that persists only on what is handed to it from outside. In the canonical taxonomy the attractlet sits left of Line 1 — it is not a recursion at all, only mimics one from outside.
An attractlet is not a kind of attractor. It is the contrast: a configuration that behaves like an attractor but is held together from outside itself. It can be bounded, it can cycle, it can even come back when you push it, which is exactly why it is so easy to mistake for the real thing. The difference is where the order comes from. A sovereign attractor produces its own; an attractlet is handed it. Remove the supply and the attractlet is gone. Each card below is one place attractlets are found.
Each card links to one example. Its small tag names what kind of example it is. A tag that cites § 7.4 means the kernel itself places that kind of thing among attractlets: its Attractlet Model class covers “ODE and PDE formalisms, idealized thermodynamic models, and externally powered inference systems,” along with simulations and numerical solvers. A tag without a citation is an authored reading, a teaching device, not a measurement.
Newton’s Method
A root-finder whose answers pull in nearby guesses and pull a nudged guess back. Every root has a basin, and the basins meet in a fractal. Stop the solver and nothing returns. Runnable now.
The Lorenz Attractor
The famous strange attractor, and an attractlet in this framing. Three equations trace a butterfly that stays bounded and never settles, but only while a solver integrates them. Runnable now.
The Carnot Cycle
Not an engine but a framework: the idealized cycle a scientist builds to study engines and search for their basin. It runs only on the reservoirs and schedule its builder supplies. Runnable now.
The Block
A 2×2 still life that persists by doing nothing at all. When a nudged block comes back, the rule rebuilt it. Runnable now.
Ferrofluid Spikes
Raise a magnetic field past a threshold and a flat pool of magnetic fluid erupts into a lattice of black spikes, each one holding its distance from its neighbours. Drop the field and it is a puddle again at once. Nothing decays. The pattern simply stops being held. Runnable now.
The Chladni Plate
Drive a plate at one frequency and scattered sand walks off the parts that are moving and piles up on the parts that are still, drawing a symmetric figure. Change the frequency and the figure reorganizes into a different one. Runnable now.
The Magnetic Pendulum
A pendulum swinging over three magnets. Colour each release point by the magnet it finally rests on and the map is a fractal, the same kind of picture Newton’s Method makes and for the same reason. Gravity drives it and friction ends it, and it owns neither. Runnable now.
The Logistic Map
One line of arithmetic applied over and over. At a low growth rate it settles on a single value, then splits into two, then four, then dissolves into chaos. There is no machinery here at all, not even a simulated one: a rule, and someone applying it. Runnable now.
The Vortex Street
Flow past an obstacle and it sheds vortices in an alternating train, each one triggering the next. You have seen it in satellite photographs, in the cloud wakes trailing behind islands. The shedding sustains itself. The flow that feeds it does not. Runnable now.
Dendritic Growth
Particles wander in at random and stick where they first touch, and what grows is a branching fractal that looks like frost on a window or the scar left by lightning. The cluster shapes what arrives at it. It does not make it. Runnable now.
Where these sit on the axis: Living Structures →, the recursive genus (base → coordination → candidate sovereign); and False Basins →, patterns off the axis entirely, neither recursive nor pulling anything home.
← Back to the Laboratory