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Hi,

I am rather new to the forum, so I do not know all of the lingo yet.

I have been playing with Kalles Fraktaler recently and have enjoyed going on random explorations and looking for interesting patterns.

One thing that has fascinated me are the complex spiral/snowflake type structures. I have noticed that structures will most often first appear with a prime number of arms and then as one zooms in, more complex arm structures will arise, often by increasing factors of two. I have been surprised that these structures will often first appear with five or seven arms and then multiply. The case of seven arm structures are quite interesting as the arms often consist of smaller seven and fourteen arm spirals. I have also seen structures that periodically increase by a factor of two, so a series of arm numbers such as 7, 14, 28, 56, 112 will arise. I've also seen odd separations, where a 28 arm structure will evolve into an 8 arm structure with four arms consolidating siz arms each, and the remaining four arms continuing.

What is the largest prime number of spiral arms that have been found in a Mandelbrot? I am curious if there are 11, 13 and 17 armed structures. Also, do complexities ever arise in multiples larger than two... For instance a 3 to 9 structure or a 5 to 15, etc...

Thanks!

Thanks Chillheimer for the reply and the video link. I just watched the video, it is great.

So, if you follow the doubling backwards, the number of arms should always originate with a prime number. The highest starting spiral I've seen is seven arms. So for spirals with less than 200 arms, the possible combinations are:

128/64/32/16/8/4/2
192/96/48/24/12/6/3
160/80/40/20/10/5
112/56/28/14/7

So my question is two fold... Has anyone seen prime spirals higher than seven? Also do the spirals ever multiply by more than two? Is there ever a case where they triple?

nope. as said, you can start with ANY number of arms. you just need to zoom deeper into the valleys. see the attached image, I haven't counted the number but it's a base period from which doubling will start if you zoom further into that area. next doubling will be 2 times the number of arms in this picture.

so if you look close at the wikipedia-image link in my first post, you will see a period 3, 5, 7 and then a period 9 bulb with 9 arms.
This 9-bulb is the base. any doubling starts from 9. 18, 36. no 4.5 or 3.
or on the right side you see a period 6 bulb as base, no 3 below it, doubling starts with 2*6.

as mentioned in my first answer in the power-2 mandelbrot set no, there will always be multiplication by 2. but in the power-x mandelbrot-set you have the multiplication * x, triple, quadruple, whatever z^x you choose as x.

Yes! That's exactly what I've been looking for! Thanks!