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Author Topic: strange area in burning ship and other asymmetric sets  (Read 1903 times)
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TheRedshiftRider
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« on: October 26, 2014, 05:09:59 PM »

I've been exploreing the asymmetric mandelbrot sets (The burning ship and related sets) a bit. There was an area I've been searching in a bit and there are some things in this area I'm not sure about and are strange to me.

This is the area Im talking about, there are two ways to get into this area:







These are some thing about this area.

-Dust/stripes above ‘'line’’. (not very surprising). When skewwing and looking into the dust it has almost the same behaviour as the normal mandelbrot.

-Mirrored mini-brots below line.  undecided

-Strange connected Julia-sets and other strange black areas. Can connected julia-sets exist outside the normal set?







-Half normal half dust/stripy Julia-sets (not surprising.)



-''Broken’’ Julia-sets (sometimes no real center). Some other julia-sets are also asymmetric and that makes that unlike most julia sets they dont always have a real center.






-Mini-brots surrounded by other ‘’black areas/rings’’. Sometimes with noise inside black parts, sometimes with dust in the black parts.  huh?







These thing can be found in the burning ship of any power and of any kind but also in all kinds of buffalos.


I think this strange behaviour is because this location is close to the 0-line. But I'm not sure.

Does anyone know what could be the cause of this?
« Last Edit: October 26, 2014, 05:17:04 PM by Toofgib » Logged

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youhn
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« Reply #1 on: October 26, 2014, 07:59:31 PM »

Ah, you did some research while exploring. Thats always nice to read/view.

But you asked perhaps the hardest question possible, roughly generalized to "Why do escape time fractals look the way they do?" The short but unsatisfying answer would be: because of the math and the chosen coloring method. On the subquestion like "why are some sets connected, while other similar fractals are disconnected" I'm not sure if there are good answers. Your possible answer "because this location is close to the 0-line" brings up the next question. Why do locations close to the 0-line (for escape time fractals that use the absolute-operation) behave that way?

And it's not just on the 0-line, but found in about all mini-copies of the main (abs-family/folding) fractals:

Bufallo mini at the real axis (Im = 0)
Re: -1.892757714829511332982988516804135
Im: 0.000000000124176591634751393692485
Zoom: 6.710886E7


Bufallo mini at :
Re: -1.736186010812808526726216
Im: 0.2566006355545148427987095
Zoom: 5.000E4


Close up of the previous one:
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Kalles Fraktaler
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« Reply #2 on: October 26, 2014, 08:54:56 PM »

I've also encountered 'black' areas that are not miniships.
They usually have a much simpler shape, round or squarish.
This movie is close to the 'neck' of the cubic burning ship 'goose' and full of round black shapes.
<a href="https://www.youtube.com/v/pKiF-xU-arI&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/pKiF-xU-arI&rel=1&fs=1&hd=1</a>

I recall someone called them monoliths. A suitable name I think.
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TheRedshiftRider
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« Reply #3 on: October 26, 2014, 08:57:28 PM »

What about the rings? And the dust?
« Last Edit: October 26, 2014, 09:08:17 PM by Toofgib » Logged

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TheRedshiftRider
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« Reply #4 on: October 26, 2014, 09:46:01 PM »

We are talking about the line of the abs function being applied on the imaginary part of the fractal. What about the real part of the fractal, shouldn't there be a visible line for the real part?
« Last Edit: October 26, 2014, 09:49:38 PM by Toofgib » Logged

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cKleinhuis
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« Reply #5 on: October 26, 2014, 10:52:02 PM »

hehe, watch the burning ship iteration visualisation, by viewing it, you see that folding real and imaginary axis brings them all to positive quadrant, and the multiplication then stretches all to positive real halve section, which might explain why there is no such features on the imaginary axis wink

watch it, take your time and try to find solutions by just watching what the math actually does!!!

its actually the reson i made those videos, so i feel perfectly fine posting it now here:
<a href="https://www.youtube.com/v/oJjjoCe5MY0&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/oJjjoCe5MY0&rel=1&fs=1&hd=1</a>

cheesy cheesy cheesy
« Last Edit: October 26, 2014, 10:55:29 PM by cKleinhuis » Logged

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nmmmnu
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« Reply #6 on: May 26, 2015, 11:35:51 AM »

Some more touristic places in Burning Ship:

https://www.flickr.com/photos/nmmmnu/17451825024/in/dateposted-public/
https://www.flickr.com/photos/nmmmnu/16598023764/in/dateposted-public/
https://www.flickr.com/photos/nmmmnu/17220464995/in/dateposted-public/
https://www.flickr.com/photos/nmmmnu/17231789505/in/dateposted-public/
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