The Attractor Explorer
Each colored dot starts somewhere completely different. But press play and they all get pulled toward the same shape — and once they're on it, they never leave. That shape is called an attractor.
Pick a shape
Hit Scatter new starts a few times. No matter where the dots begin, where do they end up?
Different starts, same destiny
This is the big surprise: the ending shape doesn't care where you started. Scatter the dots anywhere — they're all drawn to the same attractor.
A point and a loop are "tame" attractors. The strange one is special: the dots stay on the shape forever but never trace the exact same path twice.
Order you can see, futures you can't
A strange attractor is the signature of chaos. There's clear order — the shape is always there. But there's no repetition, so you can't say exactly where a dot will be later.
It's the same shape behind the Lorenz butterfly and the weather — order and unpredictability living together.
For teachers & grown-ups
Each option is a dynamical system shown as an ensemble of ~40 trajectories from random initial conditions, integrated with RK4. A point is a stable spiral (damped rotation → a fixed-point attractor). A loop is a Hopf-type limit cycle (ṙ = r(1−r²)): every nonzero start converges to the unit circle. A strange attractor is the Rössler system (ẋ = −y−z, ẏ = x+0.2y, ż = 0.2+z(x−5.7)), projected to the x–y plane — a single folded band that the trajectories settle onto but wander on forever without repeating. The shared lesson is the definition of an attractor: a set toward which nearby states evolve, regardless of starting point. The contrast between the tame attractors (point, cycle — periodic, predictable) and the strange attractor (aperiodic, sensitive, fractal) is exactly the line between order and chaos, and a natural bridge to the 3-D Lorenz tool.