Barnsley Fern

Michael Barnsley's classic affine IFS fractal simulating the self-similar frond morphology of the Asplenium adiantum-nigrum black spleenwort fern.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Stem Sway Speed 0.6

Harmonic leaf sway rate

Mathematical Formulation

63 chars medium

Analytical Equation

f_i(\mathbf{x}) = \begin{bmatrix} a_i & b_i \\ c_i & d_i \end{bmatrix} \mathbf{x} + \begin{bmatrix} e_i \\ f_i \end{bmatrix}, \quad P(f_1)=0.01, P(f_2)=0.85, P(f_3)=0.07, P(f_4)=0.07

Compact Formula

nextX = 0.85x + 0.04y, nextY = -0.04x + 0.85y + 1.6 (p = 85%)

Renderer Logic

if (r < 0.01) { nextX = 0; nextY = 0.16 * y; }
else if (r < 0.86) { nextX = 0.85 * x + (0.04 + sway) * y; nextY = -0.04 * x + 0.85 * y + 1.6; }
else if (r < 0.93) { nextX = 0.2 * x - 0.26 * y; nextY = 0.23 * x + 0.22 * y + 1.6; }

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#fern #barnsley #ifs #fractal #botany #leaves #nature

Author: Math Art Core Target: 60 FPS

Barnsley Fern

Live Parameters

Mathematical Formulation

Mathematical Tags

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