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I am studying a fractal that is defined by 4 similarities, similar to the Von Koch curve, and I am trying to verify that it does not satisfy the open set condition.

The fractal is heavily self-intersecting so it seems obvious to me that it does not satisfy the open set condition, but I am struggling to justify it. Are there any standard techniques used to prove the OSC does not hold? Or is the fact that it is heavily self-intersecting enough?

user3450230
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  • I believe this is a very difficult problem from a purely algorithmic perspective and that there is no known, general algorithm. It might be possible to address your question specifically, if you could present the four functions that comprise the IFS. – Mark McClure Apr 22 '15 at 17:51
  • To be more blunt, could you please present the IFS that you are working with? The question is interesting and potentially challenging. Given the IFS, someone might very well be interested in the challenge. Without it, certainly no one can answer your question. – Mark McClure Apr 23 '15 at 09:16
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    @MarkMcClure fair point, I'd also be interested in seeing the IFS. Especially considering that my answer only showed how to prove a set satisfies OSC. – Zach466920 Apr 23 '15 at 14:17

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