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MATH.ART
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L-System Fractal Tree

Lindenmayer botanical growth grammar producing natural dendritic fractal trees with stochastic wind turbulence and harmonic terminal leaf clusters.

Playground
60 FPS • Canvas 2D
Click + Drag to interact with field

Live Parameters

Recursion Depth 8
Branching recursion levels
Branch Length Ratio 0.72
Child branch scaling factor
Wind Gust Turbulence 1.2
Harmonic wind velocity
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Mathematical Formulation

55 chars medium
Analytical Equation
\text{Grammar: } X \to F[+X][-X]FX, \quad \mathbf{p}_{n+1} = \mathbf{p}_n + L r^n \begin{bmatrix} \cos(\theta \pm \Delta\theta + w) \\ \sin(\theta \pm \Delta\theta + w) \end{bmatrix}
Compact Formula
branch(x, y, len * ratio, angle ± Δθ + wind, depth - 1)
Renderer Logic 
const branchAngle = 0.42 + wind * 0.15;
const nextLen = length * branchRatio;
drawBranch(ctx, endX, endY, nextLen, angle - branchAngle + wind * 0.08, depth - 1, branchRatio, wind, time);
Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#tree #fractal #l-system #botany #nature #branching #leaves
Author: Math Art Core Target: 60 FPS

Export & Embed: L-System Fractal Tree

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60 FPS browser-captured stream

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<iframe src="https://art.fazleyrabbi.xyz/embed/fractal-tree" width="500" height="500" frameborder="0" loading="lazy"></iframe>
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