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
• Download
• Screenshots
• Showcase Gallery
• Images from the Book Fraxion I
• Images from the Book Fraxion II
• Licensing Information
• Commit History

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

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 org.sm.fraxion.gui.FraxionGUI

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:

• ... org.sm.fraxion.gui.FraxionGUI -locale=ukenglish
• ... org.sm.fraxion.gui.FraxionGUI -locale=usenglish
• ... org.sm.fraxion.gui.FraxionGUI -locale=dutch

The software is also hosted on

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

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.

                                                                                                                                                                                                                                     

 

 

                                                                                                                                                                                                                                 

 

 

                                                                                                                                         

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

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.

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.