Fractals are SMART: Science, Math and Art!

What are Fractals?

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

For a simple description of fractals, please download our “One Pager” (380Kb).

For more detailed info, please download our 20 page “Educators’ Guide” (7.5Mb).

Play with a fractal yourself, below:


  1. Silvershine Silvershine
    February 6, 2016    

    It explains every thing soo simply that every one can understand I love this website?

  2. Fractals4Life Fractals4Life
    January 21, 2016    

    Fractals changed my life forever. I wanted to commit suicide but then I learned about fractals. I do fractals everyday. I see fractals everyday. I fack fractals everyday. This website is amazing. I’ve sold my soul to fractals. Love them. Bye

  3. Sushi Cat Sushi Cat
    December 8, 2015    

    Once I started looking further into Fractals, I started to like them.Fractals are very interesting and artistic.

  4. Cat Sushi Cat Sushi
    December 8, 2015    

    When I first found this website I didn’t know what Fractals were. Once I started looking further into them, I started to like doing fractals. They are really cool! Fractals are very interesting and artistic.

  5. Cat Sushi Cat Sushi
    December 8, 2015    

    When I first found this website I didn’t know what Fractals were. Once I started looking further into them, I started to like doing fractals. They are really cool!

  6. Anbazhagan Anbazhagan
    November 18, 2015    

    The Sierpinski Triangle Fractal can serve as a model in Management, it appears.
    Presently, a centralised organization functions at some place with subdelegated units at other locations.
    The trickle down effect is varied, from not satisfactory to excellent.
    If the last unit also has the characteristics of the central organization, the trickle down effect in most cases would be excellent.
    Be it a production unit, sales unit, service unit, administrative unit, if like in the fractal, they imbibe the characteristcs of the basic unit, the result very well expected to be the best!

    SV Anbazhagan

  7. Mervyn Wilcox Mervyn Wilcox
    September 15, 2015    

    Absolutely awesome!!! I was helping a graduating geophysical engineer to translate his curriculum from Spanish to English and came upon the term “chaos and fractals geophysical applications.” I decided to google the word fractals and lo and behold!! I’m at the gate of knowledge. I had been told years ago that we could be part of a hair on the eyebrow of a collosal being but wasn’t able to fully grasp the meaning alltogether,although I did have an idea. Habichuelas M has really helped me out here. Thank you guys.

  8. April 15, 2015    

    google Frax for a wonderful iPad-only app that is visually stunning in its beauty.

  9. February 8, 2015    

    Now I understand that line in Frozen’s “Let It Go”. Thanks for the explanation. You are reliable.

  10. Lexieknowitall Lexieknowitall
    January 13, 2015    

    that is a really good definition! whoever made this is really smart!

  11. January 9, 2015    

    Great question, Barbara! It’s not a formal term, but we like the word “Fracticle” to describe the repeating subunit that makes up a fractal. Feel free to adopt that if it works for you 🙂

  12. Barbara Barbara
    January 9, 2015    

    Help! I’ve been trying to find the term for the basic pattern that is repeated at every scale in the fractal–as might be used the sentence, “Fractals are composed of an endless repetition of a single geometric pattern, called the [fractalus? fractalette? fractoid?] of the fractal.” Surely there is a word for this, and I am desperate to know it! Thanks so much–

  13. Sheyanne Star Sheyanne Star
    December 9, 2014    

    i love this its awesome

  14. Deb Deb
    December 9, 2014    

    I am using your wonderful site to teach my elementary art students the science AND the creative process of mono-prints! They are having a BLAST!! Thank you!

  15. Dan Dan
    November 24, 2014    

    Thank you Tom. Your response to Habichuelas Magicas was beautifully put and very clear. And of course your quote from a great mind. I can only add for Magicas, keep your feet firmly on tree ground as you reach into the stars….

  16. Tom Tom
    September 9, 2014    

    Habichuelas Magicas – I think your idea is not stupid at all, the holographic principle, and other real life theories include your ideas – and in my Scientific American, there is a new theory emerging based on the beautiful and repeating geometry of nature. Then of course you are correct that many eastern religions are huge on geometry as meaning.. I think the holographic principle and fractals have a lot in common in that in every square inch or square mile of the “film” or membrane, there is the whole contained within that. So if you Cut a piece from it, the whole is preserved… in the holograms we make, the fidelity gets less and less, like loss of resolution, but its not hard to imagine that if every inch of space is infinitely dense, the a celestial hologram would not loose fidelity. “Every particular in nature, a leaf, a drop, a crystal, a moment of time is related to the whole, and partakes of the perfection of the whole. Each particle is a microcosm, and faithfully renders the likeness of the world.” ~Ralph Waldo Emerson~ Emerson

  17. Ivichuelas Magicas Ivichuelas Magicas
    July 31, 2014    

    After a long time loving fractals, and thinking about them I got a theory that maybe sounds stupid or difficult to understand about existence in a Universal level and meaning. Considerating Fractals are the model of how naturally LIFE is created and putting it on in the macro and microcosmos would be a chance to find our planet, would be just an electron, of an atom, where the core is the sun. This atom would be part of a molecule, that is our galaxy, and with all those molecules you will find the shape of an organism, like any kind of LIFE, like the Universe.
    So if we could see the Universe from a real external perspective, maybe we would find out we live inside other human being who lives in other Universe, that is other human being, Or could be any Lifeform made up with particles, and molecules like an animal, a tree, or an apple…This could fit with the multiverse and multidimenional THEORIES, where there are infinite number of universes…
    And about the microcosmos,if we would be able to see an electron, as close as possible,maybe we would find humans on his surface, like in a planet…
    We find metaphisic and spiritul texts that say there’s a universe inside every of us, or that our planet or the universe is other kind of organism.
    The problem is we are not able to see or perceive it but in that case, we could use fractal to explain time and space like fractals, so what is 1sec for us, may be 1 year from other point of view in other place of that fractalic time, or what is 1 meter for us might be 100000km or light years from other perspective.
    I would love if somebody know about some scientis working in this kind of theory, please let me know.

  18. SAL SAL
    May 18, 2014    


  19. Sarah Sarah
    March 24, 2014    

    Awesome!!!! Love this.. 😀 Thanks! 😉

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