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Fractal Explorer

version 1.0 (32.6 KB) by

The whole Chaos in a single program.

19 Ratings



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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

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]

[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

Comments and Ratings (33)


maria (view profile)

just write it in the command window!!!!
the position of window would be adjusted perfectly


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

Laurent Cavin

Laurent Cavin (view profile)

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.


Where do we have to put the

"%callfract.m script



Thanks Shiva!

Marco Guzman


Ankur Pawar

Really good work

Roland Pfister

Roland Pfister (view profile)

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

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?

Laurent Cavin

Laurent Cavin (view profile)

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:

Best regards,
Laurent Cavin


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

Ashwin Sundar

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

Volodymyr Lytvynenko

Horia Matcaboji

Ahmas alrousan

Ajay Rawat

Excellent good work

Ashwin Sundar

Really useful

mikemelon mike

I need this very eagerly!

Shashank gupta

akalal llak


luuk buur

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:,en/.
A mirror of the ancient website is now available on:
I do not have Matlab in my current position so will usually not be able to provide assistance with this software.

Cristina Pufu

Slimane Rechoum


li xf


Zahid Ullah Khan

Its Great!!!

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.

Yunho Lee

it's amazing. you must download this!


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.

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?

Maximiliam Luppe

h.-p. b

MATLAB Release
MATLAB 6.5 (R13)

Inspired by: Fractal Fern

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