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:


23 Responses to “What are Fractals?”
  1. Caroline says:

    i love this website!! it explains everything so clearly, all the other websites I’ve been to definitely don’t! thanks so much it helped me understand!

  2. sajed says:

    Your explanation was really useful… thanks a lot…

  3. Chris says:

    I found your site from FLYlady who is a leader in helping organize and run a household. She has more than 553,000 members in her group, so don’t be surprised if your website gets a lot of traffic today.

    Love your SMART concept – I didn’t know that it was called fractals. Thank you.
    Chris – a FLYbaby

  4. rakesh says:


  5. Ashley says:

    This helped me out so much for my project, thanks a lot.

  6. Ellie says:

    Wow! This so amazing. Nice job and good music

  7. Brandon Davis says:

    this website saved my hide for a project im doing, thanks.

  8. arun says:

    thank you very much.only site which explains properly on what are fractals

  9. While I absolutely love your site, I find your definition confusing and a bit obtuse. Perhaps if you tried juxtaposing fractal patterns with their complementary opposite, linear patterns? Here linear patterns are “recognizable patterns which always repeat identically,” while fractal patterns are “recognizable patterns that always repeat differently.”
    By this definition then, things like the Mandelbrot Set are fractal whereas things like Koch snowflakes aren’t. Moreover, science based on this more rigorous definition would unfold more like a true science.

  10. steven yenouskas says:

    Fractals are sacred geometry and a hidden way nature and the universe work! They clearly demonstrate the law of correspondence:as above so below,..as below so above!!Fractals also demonstrate how the universe can both be:infinetly infinite,and infinitely finite!At the same time!!A huge paradox,but its the way our universe works. Everything is one,..just like the seers have told us for centuries!

  11. Antony says:

    I could spend hours playing with this, but it would be great to also know what mathematical equation is created from the location of each of the three buttons.

  12. Judith says:

    I first heard of fractals when I was looking for new slideshow themes for my desk top. I didn’t know what they were but they looked pretty awesome. I then saw a reference to them on the TV series “WHITECOLLAR” so I looked up the definition and then it lead me to this site. I’m here to stay – really interesting and I want to discover more – Thanks

  13. Sarah says:

    Awesome!!!! Love this.. :D Thanks! ;)

  14. SAL says:


  15. Ivichuelas Magicas says:

    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.

  16. Tom says:

    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. Dan says:

    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….

  18. Deb says:

    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!

  19. Sheyanne Star says:

    i love this its awesome

  20. Barbara says:

    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–

  21. FractalMan says:

    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 :)

  22. Lexieknowitall says:

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

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