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For Students · L-System Fractals

L-System Fractals for a k-means cluster

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a k-means cluster live below — adjust the inputs and watch it respond, right in your browser.

L-System FractalsLive

turtle graphics · rewriting rules

Controls

Presets

Iterations

A Lindenmayer system grows a string by rewriting each symbol with a rule, then reads it as turtle commands: F draw, +/− turn, [ ] push/pop. Simple rules, botanical complexity.

Reading this result: After 5 rewrites the string holds 0 symbols — each pass replaces every symbol at once, so detail multiplies exponentially, not linearly.

▶ Run in Python

Data Inspector

Angle25°

Symbols0

AxiomX

Governing equation

X \to F+[[X]-X]-F[-FX]+X, F \to FF, δ = 2 5^{\circ}, n = 5

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Frequently asked questions

Is this good for students?: Yes — this version of "L-System Fractals for a k-means cluster" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.