Consider a fractal F, generated by the set of affine transforms T, and an affine transformation A. A new set of affine transformations U can be defined such that
U is also an IFS, whose attractor is the result of applying the transformation A to the fractal F.
Many properties, e.g. the similarity dimension, of the fractal F are conserved by this technique. If F has a uniform measure, or is continous, the resulting fractal also has a uniform measure, and is continuous. However self-similarity is not conserved in all cases.
© 2001 Stewart R. Hinsley