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DIRECTORY / SANDBOXES / BARNSLEY.FERN

BARNSLEY FRACTAL FERN

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

← ALL SANDBOXES
BARNSLEY FERN IFS
150,000 PTS
POINTS / FRAME 5,000
STEM MUTATION BEND 0.00
[Iterated Function System computing affine probability transformations]
📚

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
fi(x,y)=[abcd][xy]+[ef]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 and adjust 'Stem Mutation Bend' to +0.08.

✨ 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.