Software | Java Fraxion

Fraxion (version 1.3.5) is a multi-threaded fractal exploration application, mainly providing Mandelbrot/Julia-type, Newton/Raphson-type, Magnet-type, and Markus/Lyapunov-type fractals (with arbitrary bifurcation diagrams supported for divergent fractals). It is based on the SMTools GUI framework.

Quick navigation:

List of Supported Fractals Jump to top of page

Please refer to the built-in help file for more details (formulas and examples).
Note that Fraxion supports arbitrary complex powers (instead of just real ones).

  • Classic
    • Mandelbrot/Julia
    • Mandelbar (Tricorn)
    • Randelbrot
    • Original Julia
    • Lambda
    • Inverse Lambda
    • Burning Ship
    • Bird of Prey
    • Glynn
    • Spider
  • Powers
    • Multibrot
    • Multibrot (Polynomial)
    • Multibrot (Parameter)
    • Multibrot (Inverted Parameter)
    • Multibar (Multicorn)
    • Multibar (Polynomial)
    • Multibar (Parameter)
    • Multibar (Inverted Parameter)
    • Burning Multi Ship
    • Multi Product Expelbrot
    • Multi Sum Expelbrot
    • Multi Product Exparbrot
    • Multi Sum Exparbrot
  • Trigonometric Powers
    • Sine
    • Imaginary Cosine
    • Tangent
    • Cotangent
    • Multisine
    • Imaginary Multicosine
    • Multitangent
    • Multicotangent
  • Special
    • Cactus
    • Beauty 1
    • Beauty 2
    • Ducks
    • Ducks (Secans)
    • Barnsley Tree
    • Collatz
    • Phoenix
    • Manowar
    • Quadbrot
    • Tetration
    • Tetration (dual only)
    • i of Medusa
    • i of the Storm
    • At the C-Shore
    • Logarithmic Julia
    • Hyperbolic Sine Julia
  • Newton/Raphson
    • Power
    • Power (Polynomial)
    • Fixed Polynomial 1
    • Fixed Polynomial 2
    • Fixed Polynomial 3
    • Fixed Polynomial 4
    • Trigonometric Power (Sine)
    • Trigonometric Power (Multisine)
    • Trigonometric Power (Sine Offset)
    • Trigonometric Power (Multisine Offset)
    • Nova
  • Magnet
    • Magnet Type I
    • Magnet Type II
  • Markus/Lyapunov
    • Markus/Lyapunov
    • Logistic Bifurcation
    • Jellyfish
    • Zircon Zity

Download Jump to top of page

You can download the following items:

  • The executable distribution with startup scripts (ZIP, 47.42 MiB)
  • The Java source code from the fraxion package (ZIP, 45.44 MiB, 17167/9252/12498 lines of code/comments/help)
  • The Java Docs (API documentation) (ZIP HTML bundle, 973 KiB)

There is also a direct link to the API documentation.

To run the program, download the distribution from above and execute the following command (example for Windows)

  • java -cp %CLASSPATH%;smtools.jar;log4j.jar;jlayer.jar;jna-3.5.1.jar;platform-3.5.1.jar;jhbasic.jar;fraxion.jar

Depending on available memory and type of system, you can add the following options before the -cp parameter:

  • java -server -d64 -Xmx8000M -Xms8000M -XX:+UseCompressedOops -XX:+AlwaysPreTouch -XX:+UseLargePages -XX:LargePageSizeInBytes=4m -cp ...

The GUI is multilingual; you can specify a locale as a parameter following the command:

  • ... -locale=ukenglish
  • ... -locale=usenglish
  • ... -locale=dutch

The software is also hosted on GitHub

If necessary, download the Java SE Runtime Environment 8, or for the Java SE Development Kit 8.

Screenshots Jump to top of page

Below are some screenshots from the program in action (click to enlarge).


The following photo was taken at a beach in Alicante, Spain, in August 2014, where I engraved the base formula in the sand (it's over 10 metres in length). I asked for Mandelbrot's autograph during his "Fractal Scaling in Financial Prices" lecture at the KU Leuven (23 March 2004), where he signed my copy of The Beauty of Fractals.

Showcase Gallery Jump to top of page


Images from the Book Fraxion I Jump to top of page



Images from the book Fraxion II Jump to top of page



Licensing Information Jump to top of page

Fraxion is a multi-threaded fractal exploration application, mainly providing Mandelbrot/Julia-type, Newton/Raphson-type, Magnet-type, and Markus/Lyapunov- type fractals.

Copyright 2003-2016 Sven Maerivoet

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

Commit History Jump to top of page

Note that first development started halfway 2012, with the first stint of v1.0 lasting until the end of 2012. Development for v1.1 and subsequent versions was picked up again throughout the entire year 2014.

Hash Date Subject
827a819 Nov 1 14:45:15 2016 Merge branch 'dev_bifurc' into release
03ce730 Nov 1 14:25:05 2016 Added intensity colouring to the bifurcation diagrams Fixed the mouse cursor to the bifurcation axis when navigating the complex plane for the dual inset fractal, the orbit diagrams, and the current location Recreated a sharper version of the application's background image
5ca04e3 Oct 29 17:17:02 2016 Added visualisation and controls for bifurcation diagrams of divergent fractals
896a06e Oct 7 19:04:57 2016 Merged commit
dccdebd Oct 7 18:50:18 2016 * Fixed missing icon in JHelp's window * Prevented null-pointer when help-file is not found during development
d6675cc Sep 25 01:04:34 2016 Added Ducks (secans) fractal Added Logarithmic Julia Fractal Added Hyperbolic Sine Julia fractal Added print() functionality
e95a990 Jul 19 21:59:18 2016 Moved JToolBar creation to a private method in FraxionGUI
63c9da1 Jun 13 01:30:22 2016 Fixed toolbar histogram colouring toggle when switching to default colours or binary decomposition
e4d35ec Jun 8 01:43:10 2016 Fixed the toolbar to also toggle the "Show orbits" button in special cases Fixed a problem with the about box not showing CR/LF in the licence.txt
6e5ff26 Jun 4 22:03:20 2016 Added a scale-orbits-to-screen toggle button to the toolbar
20b4713 Jun 4 18:44:23 2016 Added pixel area size to the information panel
4457efc May 26 12:54:16 2016 Changed line colour in orbit analysis panel from LIGHT_GRAY to WHITE
013a04c May 23 00:28:29 2016 Fixed a bug in incorrectly showing the Y-coordinate in grid overlay mode Changed colours for converging orbits to green and diverging orbits to yellow in orbit analyses Added the pixel area to the zoom information
f389516 May 19 01:05:05 2016 Added coordinates to the grid overlay
7474c73 May 17 13:10:50 2016 Merge branch 'develop02_zoomthumbnails' into release
7ad122e May 17 13:06:16 2016 Updated help files
74a6943 May 17 12:46:49 2016 Generated zoom thumbnails
57daab5 May 9 16:22:16 2016 Merge branch 'hotfix03' into release
18d98e2 Apr 27 11:07:52 2016 Fixed an incorrect generic in FilterSetupChooser Changed the version number in AboutBox
966e57e Apr 20 19:25:45 2016 Deactivated developer mode
b0248cc Apr 20 19:16:25 2016 Merge branch 'hotfix_improvecode' into release
31858ef Apr 20 19:08:46 2016 Performed code improvements Fixed math on constants Fixed static and final class fields Fixed possible null pointer dereferences Fixed Clone() methods Fixed unhandled class cast exceptions Fixed catching of incorrect exceptions
a95ea49 Apr 9 01:50:25 2016 Commit staged files
92cb5ff Apr 9 01:39:26 2016 Final build
a6a2a65 Apr 9 01:35:37 2016 Merge branch 'hotfix_zip' into release
1d4434c Apr 9 01:30:52 2016 Updated version number Added "Tetration", "Tetration (dual only)", "i of Medusa", "i of the Storm", and "At the C-Shore" fractals
55b1d56 Apr 7 02:40:31 2016 Merge branch 'hotfix_zip' into release
ef4b500 Apr 7 02:01:28 2016 Renamed FZIP to ZIP extension when saving and loading fractals Translated an entry in the Dutch JAR help
7ab44f4 Jun 23 22:51:02 2015 Merge branch 'develop_toolbar' into release
f654234 Jun 23 22:48:05 2015 Refactored fractal load() and save() to work with ZIP compression
6d15220 Jun 23 17:18:22 2015 Fixed toolbar Refactored KeyListener to KeyBindings Refactored fractal families into separate packages Implemented QuadBrot fractal Implemented automatic selection of maximum number of iterations Implemented distance estimation Implemented various orbit traps Updated help
fb8bd3f Feb 14 21:41:07 2015 Finished quick-access toolbar
9568e36 Feb 12 00:09:59 2015 Prepared FraxioGUI and ScreenBoundsChooser to handle a JToolBar
0bbd1e3 Feb 8 15:33:51 2015 Recreated JavaDocs and update online Help system
f999d25 Feb 8 14:50:10 2015 Reselected the menu checkbox of the last selected fractal in FraxionGUI when the user cancels the confirmation for overwriting the zoomstack
52f4e1f Feb 8 14:20:25 2015 Made FractalPanel rescale the currently rendered fractal image when the screen bounds change during loading and recalculation
596781a Feb 8 11:13:40 2015 Fixed NovaFractalIterator's escape radius (was too low)
e757a2f Feb 8 11:06:17 2015 * Optimised Newton-Raphson root detection * Fixed ScreenBoundsChooser not updating when paper width/height change
85d608c Feb 3 00:28:36 2015 * Added support for random colour maps * Refactored ColoringParameters-related methods from FractalPanel into FraxionGUI
6218e26 Jan 29 03:01:41 2015 Cleaned up FractalPanel and refactored code into FraxionGUI's actionPerformed()
613ae77 Jan 27 21:48:24 2015 Supported dual function of the navigation keys: when the overview fractal inset is shown, then the keys move the viewport around
141bf11 Jan 24 10:56:46 2015 Made a difference between calculation of striping and Gaussian Integers for interior and exterior colouring
8aec85b Jan 23 21:33:57 2015 Removed the navigation keys from the menu items and added them to KeyEvent() in FraxionGUI
4dadfa9 Jan 23 16:45:32 2015 Added a manual toggle for the suppressing of dual fractals as the inset with high iteration counts
b8d127e Jan 23 16:31:23 2015 Increased the maximum allowed number of blocks during multithreading
15eca16 Jan 23 01:26:34 2015 Merge branch 'develop1'
87fccbc Jan 23 01:21:03 2015 Update the Help system
1f596d3 Jan 22 23:59:03 2015 Added more keyboard shortcuts
996ba0d Jan 22 22:08:25 2015 Added an optional overlay grid
67cca17 Jan 22 11:03:22 2015 Removed fMaxModulus, fTotalDistance and fTotalAngle from IterationResult and affiliated classes
6a1fc86 Jan 22 02:00:53 2015 * Rearranged the rendering of supplemental information FractalPanel, so that the selection rectangle is also shown in the magnifying glass * Added modifiable memory presets to ScreenBoundsChooser
c3cfa6f Jan 21 12:32:57 2015 Enlarged main fractal overview inset and visible area rectangle
57ef9fe Jan 20 18:14:36 2015 * Fixed a bug in the GUI not disabling advanced colouring mode by default * Added XOR mode to the drawing of the current viewport in the main fractal overview inset
e40f055 Jan 20 17:36:12 2015 * Changed CTRL+W shortcut to switch showing the main fractal overview inset * Disabled advanced colouring by default
97c0301 Jan 19 21:23:49 2015 Fixed a bug in which advanced colouring was always active when loading fractal parameters from a CSV file, irrespective of its setting there
6d1f68a Jan 19 09:27:43 2015 Added functionality to FractalPanel for showing an overview of the main fractal as an inset
ebadb66 Jan 18 18:32:09 2015 Added double/halve screen size buttons to ScreenBoundsChooser
2f601a5 Jan 18 14:11:29 2015 Added a "calculation-finished" sound to the IteratorTaskExecutor
e6cbcdd Jan 15 22:01:35 2015 Merge branch 'hotfix2'
e6efcde Jan 15 21:11:25 2015 Moved ZoomStack to the package
1218446 Jan 15 17:35:09 2015 Fixed a bug that showed the complex axes on the inset fractal after it was suppressed
0b59416 Jan 14 21:48:08 2015 Updated the online help system with information on the maximum zoom depth
c8f88f8 Jan 14 18:57:22 2015 Fixed MarkusLyapunov fractals that resets the chosen colour schemes
a383938 Jan 14 17:20:18 2015 Renamed ZoomCoordChooser to ComplexBoundsChooser
0551ceb Jan 14 15:47:10 2015 * Unrolled all width * height iteration loops * Manually optimised rank order colour mapping
e8ea1ef Jan 9 02:03:47 2015 Merge branch 'hotfix1'
0699487 Jan 9 02:02:54 2015 Removed duplicate configuration of Log4j in FraxionGUI
40a4d13 Jan 9 00:54:13 2015 First public release