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BARNSLEY FRACTAL FERN

Michael Barnsley's affine transformation matrices and stochastic chaos game attractor dynamics.

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BARNSLEY FERN IFS

0 PTS

// FRACTAL SPECIES PRESETS

// COLOR & DENSITY LUT

POINTS / FRAME 5,000

STEM MUTATION BEND 0.00

PAN & ZOOM EXPLORER 1.00×

// AFFINE MATRIX EDITOR [f₁..f₄]

a (scale X)0.85

b (shear Y)0.04

c (shear X)-0.04

d (scale Y)0.85

e (shift X)0.00

f (shift Y)1.60

p (probability weight)0.85

💡 TIP: Drag canvas to pan, scroll wheel to zoom into self-similar fronds, or edit affine matrix coefficients live.

📚

RESEARCH & LEARNING VAULT // Barnsley Fern & Chaos Game Fractals

Iterated Function Systems (IFS), affine matrices, and biological self-similarity.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Michael Barnsley described the fern in his 1988 book 'Fractals Everywhere', proving that complex biological flora can be encoded into just 4 affine probability matrices.

// GOVERNING EQUATIONS

f_i(x, y) = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} e \\ f \end{bmatrix}

// BROWSER IMPLEMENTATION

Iteratively applies 1 of 4 affine 2D transformation matrices chosen according to probability distribution weights at 300,000 points per second.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOXNORMAL

1Cyclosorus Mutation

🎯 Action:Select 'Cyclosorus' preset, set 'Stem Mutation Bend' slider to 0.15 and 'Points/Frame' to 15,000.

✨ Observe:Watch the fronds curl into wind-swept spiral flora with realistic botanical curvature.

// CURATED PAPERS, RFCS & RESOURCES

Fractals Everywherebook

By Michael Barnsley (Academic Press, 1988)

The foundational textbook on Iterated Function Systems and fractal compression.

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BARNSLEY FRACTAL FERN

RESEARCH & LEARNING VAULT // Barnsley Fern & Chaos Game Fractals