Finding interesting zoom points

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Offline mikoval

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« on: September 18, 2018, 08:52:54 PM »
Hey All,

I have spent some time coming up with a coloring algorithm that I am happy with. The problem is that my zoom is coming from another fractal zoom that gave the point that was used.

I want to try applying my coloring algorithm to a new point, but am struggling to figure out how to find interesting points.

Has anyone created any tools for discovering these points? From my reading I have found misiurewicz points, which I believe are points that repeat with some period, such that it doesn't just sit on the same pattern, at least that is my understanding. Is this the right track for finding interesting points? I feel like if even if I can generate these points, most of them wouldn't be interesting, so it would be back to trial and error, just with a smaller domain. Is there a list of interesting points people have discovered? Or are willing to share some of their favorites?

Thanks for any feedback!



Offline gerrit

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« Reply #1 on: September 18, 2018, 09:13:50 PM »

Offline Fraktalist

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« Reply #2 on: September 18, 2018, 09:34:54 PM »
hi mikoval!
what do you mean with interesting points? from what perspective? artistic? mathematical?
misiurewicz points repeat the same pattern to infinity, so for my personal taste, they are boring.

there are a few simple rules where to find certain patterns like spirals n-numbered arms, how to find bifurcation points..
then there is the concept of shapestacking explained here which can be used to achive more complex patterns by combining those rules.

Offline mikoval

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« Reply #3 on: September 18, 2018, 11:59:09 PM »
Thanks for the replys and resources!  thinking "artistically interesting" however that is very subjective. I guess I am not looking for misiurewicz points then, and definitely want to do some sort of shape stacking.

I think I need to spend some time to get a better understanding of how these algorithms work if I want a chance of coming up with some interesting points, or get control over how the zoom will look.

My understanding is that you basically choose a point which will have a period until you end up at the base mandlebrot. At this point you can essentially choose a new point and repeat, resulting in the zoom. This means that the mini brots are actually accurate and maintain the properties of the full mandlebrot in terms of the shape/patterns/period.

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