Fractal Transformations

Fractal ….

chivesThe attractor of an IFS may be a Sierpinski triangle, a fractal fern or simply a filled square. With the aid of the “top” of an attractor, transformations between attractors may be established. Under simple mathematical conditions these transformations are continuous. In this way, a continuous mapping between a fractal fern and a filled rectangle can be constructed.

…. transformations

Fractal transformations to various affine IFS attractors from a filled rectangle are illustrated here. The range of each transformation is contained in the picture on the left. Chaos games with different rules are running on the left and on the right. At each step the colour from the picture on the left is ‘stolen’ and used to colour the appropriate pixel on the right.