Iterations question

[vinz]

Hi,

A question come to my mind while playing with a menger fractal object. Honestly i dunno if this is completly stupid
or if it is interesting...
i know that fractal have fractional dimension which sound weird to me. Does it be possible that fractal capable to have fractional iterations( A menger with 4.75 iterations for exemple )?
is it possible ? with what kind of algorithm? what kind of result it should give ( just an interpolation or a new object )?  

[eiffie]

Yes, no and no. Yes it is possible - not always easy - depends on the formula. If it is a simple scaling, rotation, offset then it is easy to do the fractional step at the end. The result is different from an interpolation but definitely is NOT a new object. Think of the mandelbrot set with 50 and 51 iterations - not much different.

[vinz]

Thanks for the reply Eiffie.

I think , a menger is scaling, rotation and offset, how can i achieve this for a menger ? ( i think about the menger because this is the current object i'm on ) but i think it could be done on any IFS polyhedrons i suppose, right ?.