Iterations question

vinz

Iterator

Posts: 154

« 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 )? afro


« Last Edit: July 02, 2013, 07:58:37 PM by vinz »	Logged

eiffie

Guest

Re: Iterations question

« Reply #1 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.


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vinz

Iterator

Posts: 154

Re: Iterations question

« Reply #2 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 ?.


« Last Edit: July 02, 2013, 08:22:48 PM by vinz »	Logged

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