"There's a quiet magic in the Barnsley fern-a simple set of rules that blossoms into a living, leafy pattern. The Barnsley fern is generated using an Iterated Function System (IFS): you repeatedly apply one of several affine transformations to a point, chosen at random with specific probabilities. Over many iterations, the points settle into the shape of a fern."
"Each fern point update uses one of four affine transformations of the form: f(x, y) = | a b | | x | + | e | | c d | | y | | f | The classic Barnsley fern IFS uses these transforms with associated probabilities: Project setup with canvas HTML: Create a canvas and some minimal controls. Scale mapping: Fern coordinates are roughly within x ∈ [-3, 3] and y ∈ [0, 10]. You'll map fern space to pixel space."
The Barnsley fern is produced by an Iterated Function System (IFS) that repeatedly applies one of four affine transformations to a point chosen at random according to fixed probabilities. Each affine map transforms (x,y) via linear coefficients and translations, and the weighted random selection builds the stalk, leaflets, and fine detail. Implementations map fern coordinates (roughly x in [-3,3], y in [0,10]) to canvas pixels and render tens to hundreds of thousands of points for quality. A simple HTML canvas with controls for point count and hue enables interactive drawing and animation of the fractal.
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