The Barnsley Fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book Fractals Everywhere. He made it to resemble the Black Spleenwort, Asplenium adiantum-nigrum.
We generate this fractal using Chaos game, each point constructing this fractal possess appearance probability p and it's equation:
x = a*x + b*y + e;
y = c*x + d*y + f;
Barnsley Fern is generated using four affine transformations, which are represented by the following table:
By iterating this function we get pretty good results:
My program iterates till infinity in order to see interactive animation.
You can download program source code written with C++ and OpenGL, working with Windows and MacOS X prior to 10.9, here: LINK