A fractal is not a common image, it is a mathematical object with a non-conventional third dimension that hides a universe perfectly defined by its formula. If you explore that dimension, you could surf between complex structures of great beauty where math blend into art and you will discover places never seen before which you will not be able to return to unless you write down the paths that led you there…Sergio CT
What is Fractal Geometry?
What is Fractal Geometry?
Is a quite modern and unknown theory that is providing excellent results and answers to some questions never resolved before by science. This branch of mathematics stayed unstudied due to...
This project is born to make the concept of "Fractal Geometry" known in a simple and intuitive way, it stands out especially for its software, designed to facilitate the study and experimentation with math fractals...
Software to explore Fractals
FFExplorer is a software for Windows, free and portable, that has been created under the philosophy of the project FractalFun in order to "experiment and explore fractals in a simple and interactive way"...
The complex functioning of formulas, apparently simple, is responsible of the great explosion of shapes and colours that give the fractals a high level of detail perceptible at different scales...
The "Juliter Transformation" arises during the development of new functionalities for FFExplorer and as a test of the hypothesis that fractals can be represented with a...
Orbit trap with Superformula
When I became aware of the existence of the "Superformula" equation, it seemed to me that it was versatile enough to adapt it to an orbit trap generation algorithm that would...
Mirror Plane Transformation
An example of this is the new Mirror Plane Transformation, which owes its name to the fact that, when it is applied to any complex plane fractal, the fractal unfolds into two deformed versions...
It all started in 2008, I don’t remember the date, I just remember that nothing could calm down my need of be active...
Help FractalFun is quite easy. You can translate tutorials or content, test beta versions of FFExplorer, send suggestions, etc. If you want to collaborate, please contact at
or the fantastic galleries of FFExplorer users:
Updates within the latest version (v12.3.1 - 11/08/2022)
A cellular automaton designer is added with two modes of use: rule-based or Conway's Game of Life.
The "Mirror Transformation" of the compatible algorithms is added, thus increasing their number to the 218 built-in algorithms.
The Framework version is increased to 4.8 and Net Core to 6 for greater stability and speed.
And many other improvements, which you may not see but you will notice.
In previous versions...
A new angular colouring algorithm for orbit traps is added.
Seventeen new IFS algorithms are added.
An "elements picker" that makes it easy to find palettes, themes, orbit traps, shapes, superformulas and formulas is added.
"Night Mode" is added, which changes the colours of the interface for a better experience in low light environments.
An user's formulas compiler and designer is added along with examples. With this new feature, FFExplorer has gone from being a software for fractal exploration to a software for experimentation with fractals, facilitating greatly the implementation of new ideas that take advantage of all the application features, without the need for compiling new versions of this.
Phase portrait colouring is added as a variant of escape angle colouring.
The option to create custom orbit traps using the Superformula equation is included. More information here.
The Juliter Transformation is included, which allows you to create fractals by combining the Mandelbrot and Julia methods. More information here.
Four new IRF algorithms from the Muller and Parhalley families are added.
Thread handling is improved, and the parallel computation option is added to increase the calculation speed.
A post-processing filter is added to adjust the gamma correction of final images.
Lighting algorithm support for Lyapunov-type fractals is added.
Four new fractal algorithms of the family Spider are added.
Four new fractal algorithms of the family Manowar are added.
Four new fractal algorithms of the family Lambda are added.
Random versions of the Mandelbox2D algorithms are added.
The lighting algorithm for colouring by escape time is improved.
Two new circular framing guides are added.
The option to rotate the canvas window is added.
The application code is ported to .Net Core and compiled in a separate package.
Eight new fractal algorithms of the family Magnet are added.
Default palettes are replaced by new versions generated from a color theme of the palettes form.
A parameter is added to numerically adjust the zoom level, which in combination with the central coordinates parameter will allow you to locate known areas of the fractals.
Renderer (beta) 10.1
A renderer of up to 256 Mega pixels is added and the "registration system" that gave access to this type of features in beta phase is eliminated.
Use of subprocesses to calculate fractals about 16 times faster than the previous version is implemented.
The possibility of illuminating fractals when using escape angle colouration is added.
The new IFS family is added with 18 example fractals and infinite possibilities.
Security warning when you download software
The main web browsers include a download control system that warns you about the risks when you download unknown software or software that was just created. A message like "This file type can harm your computer" does not mean that it is a malware but rather that you may adopt additional precautions. This is meant to prevent a possible attack between the creation of a new malware and its detection by antivirus systems.
It is recommended to download FFExplorer only from its official site, which is verified by several security services.
Professor of psychology in the Department of Developmental and Educational Psychology, Faculty of Education. Complutense University of Madrid - President of Spanish Society for the Giftedness Study - Headmaster of Programa Estrella (special programme for talented and gifted students)
Although math can seem a very specific subject, it is undeniable its transversality in all fields of society, science and art. Thus its incorporation as area of enrichment or extracurricular subject has been a challenge in the educational field in general and specially in the field of the most doted ones.
The idea is not teach math, but to activate the minds in order to comprehend the numeric world through high motivating activities. Fractal geometry and the project FractalFun has been the system thanks to which this challenge has been achieved in big measure.
Working with fractals, students understand the big relation between mathematics, art, rhythm and nature; they work on different scientific matters with high interest and motivation on this field. These are achievements of high educational interest without doubt.
FELIPE TORREJÓN SANJUÁN
Head of studies in Primary Education - Colegio Arcadia
Our educative model is based on the learning through skills, understanding that comprehension and learning acquisition are achieved through the content contextualization and transversality. Here is how Fractal Geometry allows to work from both fields, it relates multiple academic areas (math, science, art, ICT) and it allows to comprehend the content functionality learned at the same time by relating directly math’s concepts and procedures with natural processes.
Our year six students (Primary Education) had the great opportunity to enjoy a Fractal Geometry workshop where math blended with nature in a perfect symbiosis. We achieved to work the concept of geometry from a skill-based point of view, but above all we incited our students’ curiosity. There is no doubt of projects like FractalFun’s success in the educational field.
PILAR MUÑOZ DELEITO
Programa ADA (High Learning development) Co-director and coordinator in the Intelligence and Talent Advisory unit of the UCJC
Fractal Geometry is very attractive, motivating element for high academic efficiency students or high motivated students for scientific and artistic learning, as it is a quite modern theory which boom is answering questions never resolved by science before.
ICT has become a great tool in order to understand fractals, which makes the most of its artistic capacity but, is this science or art? It is nature interpreted under math and technology.
The project Fracfinder is a big ally in the vocational professional development; it activates the math, artistic, sociologic thinking, in short, a great tool to enrichen and develop the talent.
SANTI GARCÍA CREMADES
Mathematician, professor at Miguel Hernandez University of Elche and scientific disseminator in radio and tv programmes
Fractal geometry gets us back to the first concept of mathematics in history: a literacy science, an art full of philosophy, a beautiful and pure artwork.
Working with maths is working in something pure and that a lot. Working in fractal art is something poetic, a bridge between divine and earthly, the infinite observed with our finite eyes, the chaos seen from the biggest possible order.
FractalFun does this, something pure and poetic, what's more, from a unique technology. I can't say anymore, we are finite after all...
The aim of this contest is to «create a catalogue of certain proposals that would help to awake the enthusiasm for technology and help to bring up the early technological vocations in early stages between girls and boys aged 10 to 15»
FractalFun was awarded for its software FFExplorer in the 1st edition of the contest #ApuntasTech, brought by Centro de Supercomputación de Galicia, the Secretaría Xeral da Igualdade de la Xunta, the Colexio Oficial de Enxeñaría Informática and the Asociación de Mujeres Investigadoras y Tecnólogas.
Extract from the conclusions of the research work carried out by two students belonging to the Batxillerat Científic de l'Institut Joan Brossa (Barcelona)
This work has radically changed the way we perceive the real world, since after knowing fractals it is difficult not to appreciate them everywhere.
To define their characteristics we learned to use FFExplorer, a tool that has allowed us to see how they are formed, which has represented a very important part of the work.
At the end, those irregular figures that we thought we would never understand turned out to be extremely simple. We observe that they have many applications, and that most people are not aware of their importance.
We have learned a multitude of things that will certainly help us in our future.
What is Fractal Geometry?
Fractal Geometry is a quite modern and unknown theory that is proving excellent results and answers to questions never resolved before by science.
This branch of mathematics stayed unstudied due to the quantity of calculi necessary to obtain results; today it’s giving new and unexplored territories to experiment thanks to ICT’s advance, what have allowed to automatize and speed up these calculi.
From a mathematical point of view, we are talking about the best approximation up to date in order to describe and understand the designs created by nature, which also lets create amazing digital pieces of digital art, commonly known as "Fractals".
A fractal is just a graphic representation of a mathematic function’s behavior, handled in a special way, but it was just these graphics features (so similar to nature structures features) what made this type of geometry to be considered as « the language used by nature in order to reveal its secrets ».
Nowadays, this cutting-edge theory is being applied to technology, medicine, architecture, astronomy, economy, sociology, and many more, what offers multiple possibilities… making obvious that, more that offering extracurricular contents to our students, Fractal Geometry allows to stablish didactic connections between very different areas and subjects, creating an ideal setting for the student to choose the most desired path during the learning process.
The FractalFun Project* starts in the context described previously, designed to make the concept of "Fractal Geometría" known in a simple and intuitive way. Its highlight is the software FFExplorer, in constant evolution since 2010 in order to facilitate the study and experimentation with fractals.
Nowadays, different Educational Enrichening Programs are supported on FractalFun and bet for this cutting-edge subjectas vehicle for the development of new abilities and contents in their students., with the aim of providing them of new abilities that letrecognise and apply geometric ideas in areas out of math. Like art, for example, nature, everyday life… what will help them in the future to find creative solutions to real problems.
Last but not least, this project has also the aim of making students to develop knowledge that will give them superior skills to go back when needed in the future and solve possible situations or problems yet to be solved within different areas of study or work.
The following videos show some of the activities carried out by the students of the Fractal Geometry Area:
For more information on the project please contact at
Or you may have a plan already and you only need a "Software to explore Fractals"
(*) This project and its software were called "Fractfinder" and "Explorador FF" till 2018.
Software to explore Fractals
FFExplorer is a software for Windows, free and portable, that has been created under the philosophy of the Project FractalFun in order to experiment and explore fractals in a simple and interactive way.
If you are going to explore fractals for the first time, the software will offer you the possivbility to forget about numbers and formulas. You will be able to discoverand enjoy using just your mouse over the images.
If this is not your first contact with fractals, this software will offer you the possibility to use it in a more advanced way. You will be able to change parameters and behaviours of logarithms in order to create an infinite variations of the original fractals.
This software has been designed with a desktop interface so you can organize the canvases and tools to your liking when working, so you will always have everything you need visible and handy.
FFExplorer includes different fractal algorithms, as well as several colouring methods. You can also find multiple tools and different graphic designers based on maths, like a fractal projector over Riemann spheres, a fractal kaleidoscope, etc.
« FFExplorer is easy to use, versatile and adaptable. You can get very varied fractal images that can be used or different purposes, designing surprising animations, or create Fractal Art of high quality. Once the image is generated you have the option to use a graphic editor to change it but I personally prefer to look for the final aspect of the image just by exploring the fractal, using it without editing, so it keeps and shows all the math’s intact essence.
Nevertheless, a part from being a software that allows a high level of control in order to generate beautiful images with any aspect you’d like, FFExplorer is true to its name as it allows to explore fractals, and that is an amazing experience. When I start I cannot seem to stop… »
ElenSegu, expert in design and Fractal Art
The concept of art admits several interpretations, what makes really hard to define it, but one could say that most of them talk about its esthetical and communicative abilities to transmit ideas and feelings, in other words, everything to do with our emotional part...
It seems contradictory to talk about creating art through maths, a subject that remind us of words like as "precision", "calculi", "análysis"... cold concepts linked to the rational thinking and, in appearance, incompatible with art.
However, this has changed thanks to Fractal Geometry: a fractal is a graphic manifestation that represents the behaviour of a mathematical formula, which author has experimented till the desired aspect. That experimentation consists on the numeric adjustment of certain parameters, the introduction of little transformations and the good treatment of the colouring. With all that we get an approachable graphic environment which, a part from the planes' two dimensions, has a third dimension (non-conventional) only accessible when zooming. It is in this virtual world where the creator can freely move and look for the most desired area and framing in order to finish the piece of art.
Fractal art has some very exclusive features:
Complexity. The complex functioning of formulas, apparently simple, is responsible of the great explosion of shapes and colours that give the fractals a high level of detail perceptible at different scales. This makes a piece of art with big proportions show very different details depending on the distance from where it is been watched, being more noticeable its self-similarity feature and the third dimension effect.
Perfection. The aspect of a fractal image is perfectly defined by the algorithm's configuration that draws it; this means that the formula and the numeric values set there are a unique distinguishing mark exclusive of the image. Knowing this data allows redrawing it as many times as wished, for example to keep on working on it, or to generate a copy from the original at higher resolution without losing quality (actually, it improves its definition).
Exclusivity. The formula that draws a fractal is very sensitive to the values in its parameters, so a slight variation in any of them produces a completely different image. Thanks to this, it is close to impossible to draw a fractal image again if you do not know the formula and the exact values employed originally, what prevents falsifications and allows proving who is the author of the image.
If you found this interesting, you can visit the Social Networks of FractalFun: