Notes on Barnsley Fern

An affine transformation on the plane is a mapping T that preserves collinearity and ratios of distances: given two points A and B, if C is the middle of the segment [A,B] then T (C) is the middle of the segment [T (A), T (B)]. Translations, contractions, expansions, reflections, rotations, are all particular cases of affine transformations. In general, an affine transformation T maps a point (x, y) to a point (x′, y′) such that ( x′ y′ ) = ( a b c d )( x y ) + ( e f )