Logo by kr0mat1k - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. March 28, 2024, 11:48:51 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1] 2   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Shortcuts in juliasets  (Read 7223 times)
0 Members and 1 Guest are viewing this topic.
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« on: June 19, 2015, 08:31:33 AM »

Yesterday I posted an image of a dense julia-set (http://www.fractalforums.com/kalles-fraktaler-gallery/simple-density). I'm going to explain how I did this.

Morphing is frequently discussed on this forum and the rules are clear about how it works:
Quote
The pattern is doubled and wrapped around the point, and also the area nearest the point is magnified.

But not just the pattern of the juliaset is doubled but also the points you have zoomed into in previous stages of the morph. Look at the 4th image here to see what I mean:
http://imgur.com/a/ShV0U


 These points contain the previous stages of the morph. And can be used as a shortcut to a next julia-set. In general the shortcuts that are closer to the center of the juliaset are shorter. Look at the 4th image again. The center is of course the fastest but it only doubles. The point close to the outside of the juliaset contains the julia-set of image 1. The one closer to the center contains the one of the second images. And the one closest to the center contains julia-set 3.

Basically what I did with the image I made yesterday was I just zoomed into the shortcut which was close to the center. I did this several times and the julia-set became more complexe and it did not need a lot of zooming. And I think the rendertime is also greatly reduced compared to deep complex morphs.

The location of the image is in the file in as attachment.

* lost.rar (0.95 KB - downloaded 304 times.)
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
Chillheimer
Global Moderator
Fractal Schemer
******
Posts: 972


Just another fractal being floating by..


chilli.chillheimer chillheimer
WWW
« Reply #1 on: June 19, 2015, 09:13:20 AM »

I can confirm your finding. complexity raises really fast this way
I have to say that I already did this, but more intuitivley than in the analytic way you did it. Fascinating what happens when you really repeat this very often.

I'm still trying to find out how and why this works.
Unsure if I use the mathematical correct words to desribe this:
I guess it's simple periodic doubling (but of an already complex shape).
Íf you doulbe an already very complex part of the julia set (instead of e.g. a simple spiral at the beginning) you double that complexity. its like 128² compared to 2².
and if you repeat this process all over the complexity must rise much faster than if you take the long route.
though of course you will reach 128 too when starting with 2². but at much deeper zoom depth.
it might not "speed up" the distance to the next minibrot, but the minibrot is much more complex than without.

the only "downside" to this is that you will only repeat the simple patterns you used in the very beginning, the shapestacking phase.
with the long route you can still change details in your zoom path at any time.
details that of course show up later. but those will be subtle details in complex deep julia-sets like your example from yesterday. so it doesn'T really matter in that context.

I guess you could call it level-2-shapestacking. shapestacking of julia-sets. smiley

very interesting. nice share. smiley
Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #2 on: June 19, 2015, 09:53:53 AM »

I can confirm your finding. complexity raises really fast this way
I have to say that I already did this, but more intuitivley than in the analytic way you did it. Fascinating what happens when you really repeat this very often.
Unsure if I use the mathematical correct words to desribe this:
I guess it's simple periodic doubling (but of an already complex shape).
Íf you doulbe an already very complex part of the julia set (instead of e.g. a simple spiral at the beginning) you double that complexity. its like 128² compared to 2².
and if you repeat this process all over the complexity must rise much faster than if you take the long route.
though of course you will reach 128 too when starting with 2². but at much deeper zoom depth.
it might not "speed up" the distance to the next minibrot, but the minibrot is much more complex than without.

the only "downside" to this is that you will only repeat the simple patterns you used in the very beginning, the shapestacking phase.
with the long route you can still change details in your zoom path at any time.
details that of course show up later. but those will be subtle details in complex deep julia-sets like your example from yesterday. so it doesn'T really matter in that context.

I guess you could call it level-2-shapestacking. shapestacking of julia-sets. smiley

very interesting. nice share. smiley
Thanks for your reply. What you say is correct I think. Though, I think it is possible to create a bit more complex shapes by changing which shortcut you use at every stage of the morph, this will take more depth but the shapes will be more complex.
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #3 on: June 19, 2015, 01:28:49 PM »

I tried to find a more complicated location:


For this one I used varied shotcuts.

* simple density v2.rar (0.51 KB - downloaded 291 times.)
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
Chillheimer
Global Moderator
Fractal Schemer
******
Posts: 972


Just another fractal being floating by..


chilli.chillheimer chillheimer
WWW
« Reply #4 on: June 19, 2015, 01:50:01 PM »

hehe, I know that guy!
http://chillheimer.deviantart.com/art/I-see-you-500674399
Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #5 on: June 19, 2015, 02:12:02 PM »

laugh Nice one.

One other thing I found which some may consider good or bad is that the set contains in this context ''eyes''. I think it looks cool in most cases but you probably have those with very deep morphs with the ''normal'' method.
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #6 on: June 30, 2015, 01:55:50 PM »

it might not "speed up" the distance to the next minibrot, but the minibrot is much more complex than without.

I'm still not sure about this. I did some test and some had a shorter distance to the minibrot. (I used a method of just zooming, so not very accurate) I think it depends on whether a shortcut is taken in a juliaset as last part of the morph before it starts doubling. And maybe also if in the morph other minibrots have been passed or not.
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #7 on: June 30, 2015, 10:44:14 PM »

I found out that fractal universe made a video with this technique a year ago.
<a href="http://www.youtube.com/v/4Yg1SeFjOik&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/4Yg1SeFjOik&rel=1&fs=1&hd=1</a>
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
Adam Majewski
Fractal Lover
**
Posts: 221


WWW
« Reply #8 on: July 01, 2015, 03:17:30 PM »

Is it similar techique as in :

http://mathr.co.uk/blog/2015-05-18_two_spirals_out.html

?
Logged
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #9 on: July 01, 2015, 03:26:49 PM »


Almost. The main thing im talking about is the shortcut near the center of the julia set. The main ''eye'' near the center as I call it.
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
Dinkydau
Fractal Senior
******
Posts: 1616



WWW
« Reply #10 on: July 28, 2015, 03:55:52 PM »

If you deviate from your path you can basically "continue" the old path from that shortcut you mention, if I understand it correctly. It saves a ridiculous amount of zoom depth. It can be used to achieve more complex results than otherwise possible but you have to sacrifice some levels of choice. In this image I used the method to make an S that contains shapes while still being at only relatively low zoom depth (in perturbation era understanding at least).


"Evolution of trees" is a more complex version of this method, but it's still the same kind of zoom method. It works by going into the shortcuts and morphing the julia sets there.
Logged

TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #11 on: July 30, 2015, 01:35:20 PM »

Thanks.
I think that morphing for images is more appropriate without shortcuts. But for movies the shortcuts are great.
Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
claude
Fractal Bachius
*
Posts: 563



WWW
« Reply #12 on: July 30, 2015, 02:30:03 PM »

Binary decomposition colouring can help to find the shortcuts (including the central minibrot) when you have very thin filaments - follow the lines that start further out, they end on the tips of filaments surrounding a shortcut.  For these images I used an edge detection filter on integer iteration count and whether the final angle was positive (these create the grey grid), the filaments are coloured with distance estimate.

First 2 images:
Code:
real=-1.9963810738192679122181468389365117014665310349376e+00
imag=7.4685300102574615047563223151397682359866402430498e-06
radius=1.2325951644078309e-32
Second 2 images, zoomed in slightly below left of center:
Code:
real=-1.99638107381926791221814683893651199888802191225853e+00
imag=7.46853001025746150475632231492495186779320342460899e-06
radius=7.7037197775489434e-34


* 2015-07-30_shortcut_decomposition_1a.jpg (76.04 KB, 640x360 - viewed 697 times.)

* 2015-07-30_shortcut_decomposition_1b.jpg (86.51 KB, 640x360 - viewed 653 times.)

* 2015-07-30_shortcut_decomposition_2a.jpg (4.85 KB, 640x360 - viewed 646 times.)

* 2015-07-30_shortcut_decomposition_2b.jpg (16.86 KB, 640x360 - viewed 690 times.)
Logged
quaz0r
Fractal Molossus
**
Posts: 652



« Reply #13 on: May 15, 2016, 10:30:37 PM »

have you guys posted any videos which clearly depict what it is exactly you are talking about here?
Logged
TheRedshiftRider
Fractalist Chemist
Global Moderator
Fractal Iambus
******
Posts: 854



WWW
« Reply #14 on: May 15, 2016, 10:32:55 PM »

Of course:

<a href="https://www.youtube.com/v/x2g_dlsX5k4&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/x2g_dlsX5k4&rel=1&fs=1&hd=1</a>
« Last Edit: May 16, 2016, 09:46:02 AM by TheRedshiftRider » Logged

Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting. nerd
Pages: [1] 2   Go Down
  Print  
 
Jump to:  


Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.152 seconds with 23 queries. (Pretty URLs adds 0.008s, 2q)