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Fractal Explorer

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28 Jul 2004 (Updated )

The whole Chaos in a single program.

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Description

Fractal Explorer

GUI-based program for exploring and studying the most common form of fractals, chaotic systems and fractional dimension systems. An overview of the features with a small introductory text is available at

http://ltcmail.ethz.ch/cavin/fractals.html

The usage is straightforward. Type "fractal_explorer", and the main window will be opened and the Mandelbrot Set will be drawn. All features are available via menus and buttons. Information is given on the bottom-left corner of the figure, while tips and information will appear on the left side of the figure when user input is required/possible. For most functions, dialogs will allow introducing user-defined parameters or equations for the calculation. Most dialog contains a button labeled "Cool Params" or "Examples" - this will propose a set of parameters leading to a chaotic behavior (as it is sometimes difficult to find a good parameter set); when only one typical set of parameter is customarily used, it will be given by default the first time the function is called.

The features include:

- Logistic Equation [1]
- Real 2D Attractors:
    - Henon Attractor [1]
    - Pickover System [1]
    - Arbitrary Quadratic Map [1]
- Real 3D Attractors:
    - Lorenz Attractor [2]
    - Roessler Attractor [2]
    - Limited Quadratic Map [2]
- Complex Maps:
    - Mandelbrot Set [1,5]
    - Julia Sets [1,3,5]
    - Arbitrary Polynomial Newton-Raphson
      Attraction Basins [1,5]
    - Barnsley's Tree [1,5]
    - Arbitrary Mandelbrot and Julia-based
      Sets [1,5]
- Quaternions:
    - Mandelbrot and Julia Sets [2]
- String Systems:
    - Lindemayer Systems Single Rule
    - Lindenmayer Systems Multiple-Rules
    - Plant-like systems:
        - Barbsley's Fern [4,6]
        - Fractal Trees
    - 3D Systems
        - 3D-Multiple-Rules Lindenmayer
          Systems [2]
        - Menger Sponge [2,4]
- FOlded Plans:
    - Mesh grids [2]
    - Fractals Clouds
    - Fractal Landscapes [2]

Notes:
[1] Interactive Zooming
[2] Interactive 3-D View
[3] Julia explorer with on-the-fly previews
[4] Limited to built-in parameters
[5] Include the function Make-It-3D?
[6] Equations taken from Brian Mearns's "Fractal Fern"

For more information, see http://ltcmail.ethz.ch/cavin/fractals.html#SOFT

Acknowledgements

Fractal Fern inspired this file.

MATLAB release MATLAB 6.5 (R13)
Other requirements Tested only with R13.
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Comments and Ratings (33)
19 Jun 2014 maria

hq=fractal_explorer();pos=get(hq,'position');
set(hq,'position',[0,0,pos(3),pos(4)])
just write it in the command window!!!!
the position of window would be adjusted perfectly

21 Mar 2012 Rodrigo

Thanks! finally got it right hehehe. Awesome program btw!

15 Feb 2012 Laurent Cavin

>Rodrigo
I guess you simply type it into the command prompt. This commands will open fractal_explorer and move the window. You can also save it under a new name (such as callfract.m) and then use the command "callfract" instead of "fractal_exporer" to start it.

24 Sep 2011 Rodrigo

Where do we have to put the

"%callfract.m script
hq=fractal_explorer();pos=get(hq,'position');
set(hq,'position',[0,0,pos(3),pos(4)]);"

code?

01 Jun 2010 Stephen

Thanks Shiva!

17 Jan 2010 Marco Guzman

Sweet

04 Aug 2009 Ankur Pawar

Really good work

23 Jul 2009 Roland Pfister  
08 Apr 2009 shiva Banerjee

Solution to:
"I only get a part of a window in the corner of my screen, and I cannot move it, nor reach any buttons and so on"

soluition: 'use 'callfract.m' to reset window position

%callfract.m script
hq=fractal_explorer();pos=get(hq,'position');
set(hq,'position',[0,0,pos(3),pos(4)]);

11 Feb 2009 Pierre Bushel

I'm very interested in the use of fractals for determining the dimension of a self organizing map (SOM). Thanks for providing a wonderful collection of information. I have data consisting of continuous measurements with the number of features (p) >> the number of attributes (n). Using this two dimensional framework, is there Matlab code that can use fractals to estimate the topology of the data (in terms of the number of clusters) for subsequent analysis with SOM in an N by M dimension? In other words, can fractals estimate N and M from the data?

05 Jan 2009 Laurent Cavin

Dear all,
thanks for the incredible number of downloads, and sorry that it does not work for some of you. As mentioned, I do not have Matlab in my current position, so I won't be able to help - if anybody wants to post a fix for newer releases, be my guest.
I moved again the website with an introduction on Chaos and the images generated by this program to:
http://www.cavin.name/CSE/en/Fractals/A_trip_in_the_fractional_dimension/

Best regards,
Laurent Cavin

29 Oct 2008 Dr. Jens Koopmann

Laurent,

I am sorry to say that the program does not run on my Matlab version.
I think the GUI is to big for my screen and I can not move/drag the GUI to get it work.

Kind regards
Jens

02 Oct 2008 Ashwin Sundar

Great relief in coding fractional dimensions...., Thank u

28 Sep 2008 Volodymyr Lytvynenko  
13 May 2008 Horia Matcaboji  
14 Mar 2008 Ahmas alrousan  
26 Feb 2008 Ajay Rawat

Excellent good work

22 Feb 2008 Ashwin Sundar

Really useful

23 Jan 2008 mikemelon mike

I need this very eagerly!

11 Jan 2008 Shashank gupta  
17 Sep 2007 akalal llak

hi

22 Aug 2007 luuk buur  
04 Apr 2007 Laurent Cavin

Hi - for your information, my old web site on ETH is dead. You can find the information about fractals on my new website: http://www.cavin.name/jmla/content/blogcategory/15/28/lang,en/.
A mirror of the ancient website is now available on: http://cse.cavin.name/fractals.html#SOFT
I do not have Matlab in my current position so will usually not be able to provide assistance with this software.

01 Nov 2006 Cristina Pufu  
28 Sep 2006 Slimane Rechoum

Great.

03 May 2006 li xf

good

20 Feb 2006 Zahid Ullah Khan

Its Great!!!

02 Nov 2005 TingTing Li

I also have the problem: Get a part of a window in the corner of my screen, and I cannot move it, nor reach any buttons and so on. Can anybody tell me how to solve it by e-mail.Thanks a lot.

29 Oct 2005 Yunho Lee

it's amazing. you must download this!

06 May 2005 AMEJDOUBI KARIM

dear sir,
i have some problems in doing a matlab program to obtain the geometric forms of the " koch snowflake" and "regular pentagon" in a squared networking.
I ask you sir, if its possible to help me in this and send me some program similar to the one i desire to do.

thank you sir for your help always.
AMEJDOUBI

04 Dec 2004 Per Sundqvist

I only get a part of a window in the corner of my screen, and I cannot move it, nor reach any buttons and so on. Is this a bug?

02 Nov 2004 Maximiliam Luppe  
10 Aug 2004 h.-p. b  

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