FRACTFINDER

« Being a language, mathematics may be used not only to inform but also, among other things, to seduce... »
Benoît Mandelbrot, creator of the Theory of Fractals
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 were math blend into art and you will discover places never seen before which you will not be able to return unless you write down the paths that leaded 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...
read more

Fractfinder Project

Fractfinder Project

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...
read more

Software to explore Fractals

Software to explore Fractals

Explorador FF is a software for Windows, free and portable, that has been created under the philosophy of the project Fractfinder in order to "experiment and explore fractals in a simple and interactive way"...
read more

Fractal art

Fractal art

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...
learn more

GALLERY

Here are some fractal images generated with Explorador FF, to see many more examples visit the social networks of Fractfinder.

Explorador FF

Software for the interactive exploration of fractals

Updates within the latest version (09/23/2018)

Fractal algorithms
It adds a new Mandelbox 2D algorithm that allows to move the cutting plane.

Colouring algorithms
More possibilities of customizing the colouring algorithm based on the scape angle.

Parameters
It adds the possibility to modify parameters before constant in the fractals: bailout, tolerance, scale...

And many other improvements, which you may not see but you will notice. More information...


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 Explorador FF only from its official site, which is verified by several security services.

Descargas


Explorador FF in figures
(09/23/2018)
64
Algorithms
22
Tools
36
Orbit traps
10329
Official downloads

Opinion

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 Fractfinder 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.

LUZ PÉREZ-SÁNCHEZ

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)

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 Fractfinder’s success in the educational field.

FELIPE TORREJÓN SANJUÁN

Head of studies in Primary Education - Colegio Arcadia

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.

PILAR MUÑOZ DELEITO

Programa ADA (High Learning development) Co-director and coordinator in the Intelligence and Talent Advisory unit of the UCJC

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 ».

Hoja de plátano

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.

If you work in a school you may be interested in the “Fractfinder Project
Or you may just be looking for a fantastic "Software to explore Fractals”.


Fractfinder Project


The Fractfinder 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 Explorador FF, in constant evolution since 2010 in order to facilitate the study and experimentation with math fractals.

Nowadays, different Educational Enrichening Programs are supported on Fractfinder 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.

Taller de Geometría Fractal

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.

For more information on the project please contact at "contacto@fractfinder.es"
Or you may have a plan already and you only need a "Software to explore Fractals"


Software to explore Fractals


Explorador FF is a software for Windows, free and portable, that has been created under the philosophy of the Project Fractfinder 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.

Explorador FF

Explorador FF 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.

« Explorador FF 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, Explorador FF 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

Here you can download the last version of "Explorador FF"
Here you can see "Explorador FF in figures"


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.

Arte Fractal Sergio CT

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 this gallery of "Fractal art in high resolution"