Title: Iterations question Post by: vinz on July 02, 2013, 07:47:19 PM 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 )? O0 Title: Re: Iterations question Post by: eiffie on July 02, 2013, 08:09:53 PM 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.
Title: Re: Iterations question Post by: vinz on July 02, 2013, 08:19:37 PM 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 ?. |