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L-system fractal generator

Grow fractals from a Lindenmayer system: an axiom string rewritten by production rules, then drawn as turtle graphics. Type your own axiom, rules and angle, or load presets for the Koch snowflake, Heighway dragon, fractal plants and trees — each one blossoms from a handful of symbols.

Related tools

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System of Inequalities GrapherGraph a system of linear inequalities in x and y: shade the feasible region, draw each boundary (dashed for strict), list the region's vertices and tell you whether it is bounded, unbounded or empty.System of Linear Equations SolverSolve 2×2, 3×3 and 4×4 linear systems by Gaussian elimination, Cramer's rule or the matrix inverse — with the determinant, step-by-step working, and detection of no-solution and infinite-solution cases.System of Nonlinear Equations SolverSolve 2- or 3-variable nonlinear systems (polynomial, trigonometric, exponential) with multivariate Newton's method — enter equations as text, set a starting guess, and surface every real solution with its residual.System of ODEs SolverSolves 2×2 and 3×3 linear systems x′ = Ax with eigenvalues, eigenvectors and the closed-form general solution, classifies the fixed point (node, spiral, centre, saddle, degenerate), and integrates arbitrary nonlinear 2D systems numerically with a phase portrait.3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.Annulus (ring) area calculatorCompute the area of a ring from its outer and inner radius.Aquarium volume calculatorCompute the water volume of a rectangular aquarium in litres and gallons.

L-system fractal generator works straight from this page — free, instant, nothing to install. It covers an axiom string rewritten by production rules, then drawn as turtle graphics. Type your own axiom, rules and angle, or load presets for the Koch snowflake, Heighway dragon, fractal plants and trees — each one blossoms from a handful of symbols — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is L-system fractal generator?

Grow fractals from a Lindenmayer system: an axiom string rewritten by production rules, then drawn as turtle graphics. Type your own axiom, rules and angle, or load presets for the Koch snowflake, Heighway dragon, fractal plants and trees — each one blossoms from a handful of symbols.

What does a concrete case look like?

F → F+F−F−F+F (Koch) — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in an axiom string rewritten by production rules, then drawn as turtle graphics. Type your own axiom, rules and angle, or load presets for the Koch snowflake, Heighway dragon, fractal plants and trees — each one blossoms from a handful of symbols. Change any of them and the output follows immediately.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

How is L-system fractal generator different from System of Inequalities Grapher?

They sit next to each other but answer different questions: System of Inequalities Grapher is the one to open when you need it to graph a system of linear inequalities in x and y: shade the feasible region, draw each boundary (dashed for strict), list the region's vertices and tell you whether it is bounded, unbounded or empty. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

System of Linear Equations Solver is the closest one after this: Solve 2×2, 3×3 and 4×4 linear systems by Gaussian elimination, Cramer's rule or the matrix inverse — with the determinant, step-by-step working, and detection of no-solution and infinite-solution cases.

What else is worth having open alongside it?

System of Nonlinear Equations Solver and System of ODEs Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The formulas are the classical ones and the results are exact to the precision shown — geometry does not change with the year or the country, so nothing here needs updating.

Further reading

All guides →
How-toHow Much Substrate Does an Aquarium Need? Depth, Weight and Grain SizeThe depth follows the job: a bare display, a planted tank whose roots need room, an under-gravel plate. Then comes the number people are unprepared for — substrate is what puts a filled tank past what a piece of furniture can hold. Plus why fine sand compacts and coarse gravel traps waste.ExplainerHow Many Fish Can a Tank Hold? The Inch-per-Gallon Rule Is WrongEvery stocking calculator implements a length-per-volume rule, and waste output scales with body mass, not length. A fish twice as long makes nearly five times the ammonia. Run through the tool's five methods, the same tank comes back holding anywhere from 6 to 12 fish.How-toWhat Wattage of Heater Does an Aquarium Need? Volume Is Only Half the AnswerThe same tank needs a 100 W heater in a warm flat and 300 W in an unheated room. The variable is the gap between the water and the room, which most rules of thumb drop entirely. Plus why two smaller heaters beat one big one, and where this calculator's recommendation stops being trustworthy.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.
L-system fractal generator — OneKitly