BARNSLEY FRACTAL FERN
Michael Barnsley's affine transformation matrices and stochastic chaos game attractor dynamics.
BARNSLEY FERN IFS
150,000 PTS POINTS / FRAME 5,000
STEM MUTATION BEND 0.00
[Iterated Function System computing affine probability transformations]
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ACADEMIC & ALGORITHMIC REFERENCERESEARCH & LEARNING VAULT // Barnsley Fern & Chaos Game Fractals
Iterated Function Systems (IFS), affine matrices, and biological self-similarity.
// 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 SANDBOX
1Cyclosorus Mutation
π― Action:Select 'Cyclosorus' preset and adjust 'Stem Mutation Bend' to +0.08.
β¨ Observe:Watch the fronds curl into wind-swept spiral flora with realistic botanical curvature.