What are fractals? Recursive geometry in nature

Ranked #1,622 in Home & Garden, #25,249 overall

On the left you see a version of the most famous fractal of all time: the Mandelbrot fractal. However closely you zoom in, you'll always see roughly the same pattern. That's what defines a fractal. They are defined by a relatively simple mathematical formula.

From a mathematical perspective what's important is that these equations, though simple, don't produce a line the way a linear equation does, or a parabola or anything like that.

I won't try to explain the math of this, but a few simple examples may make the concept visually clear.

Sierpinski Equilateral Triangle

The point here is that however much you zoom in, you always see the same thing. These Sierpinski triangles can easily be made by anybody who has enough mathematical skill to make an equilateral triangle. All it takes is a good large piece of paper and pencil and a Protractor or something else to measure angles with and draw straight lines.
powered by Youtube
Someone actually drawing the Sierpinski Triangle: a simple fractal.
powered by Youtube

Von Koch Snowflake Curve

Similar to the Sierpinski Triangle in concept, the Von Koch snowflake is a simple fractal. The poor guy presenting this hopefully got over his shyness or decided never to become a presenter. It's the best video I could find with the Von Koch Snowflake.
powered by Youtube

Tree fractal: math in nature

This animation based on a simple C++ program shows how close trees are to being shaped on the basis of the simple math of fractals.
powered by Youtube

More fractal pictures

Loading

More fractal geometry

Loading

Now, do you understand fractals?

submit

More science, math and education

brain
Brainetics Math Games and Memory System

Brainetics is an aid for students, teachers, parents, and adult learners who would like to improve their mathematics and memory skills. It also helps one...


fractals
What are fractals? Recursive geometry in nature

On the left you see a version of the most famous fractal of all time: the Mandelbrot fractal. However closely you zoom in, you'll always see roughly the...


LEGO City Police Station
LEGO City Police Station

LEGO City Police Station is a real delight for all LEGO lovers - be they young or grown ups. This large LEGO set will help you create an entire Police Station...


philosophy
John Hick - philosopher of religion

An introduction into the philosophy of John Hick a noted religious philosopher using quotes. Philosophers of religion know John Hick's pluralistic ...


paper models
Origami Phizz Units - math crafts at home

This is a lens devoted to showing and explaining what a PHiZZ unit is and how much fun can be had from them. PHiZZ unit stands for 'Pentagon, Hexagon, Zig Zag'...


Spirituality
Rupert Sheldrake

Biologist known for his theory of 'morpho-genetic fields'. These fields make learning something easier once it's been learned before by someone else. This ...


Astronomy
Best Astronomy Software

Astronomy is one of the oldest Sciences. From the ancient Sumerians to the Modern Age human beings have always been fascinated by what the stars have to...


Best gift ideas
Best Beautiful Fractal Books

Fractals are a fascinating field of Mathematics in which patterns get repeated in ever smaller form. What's more, they turn out to describe very different...


Chess Sets
Best Fun Cool Specialty Chess Sets

Chess is a board game that has been around for thousands of years. Experts believe that Chess originated in either India or Persia. It is a game that help develop...


consciousness
Videos about NDEs - Near Death Experiences

Videos about Near Death Experiences: both reflection about the topic, as well as testimonies. From Christian to atheist interpretations of NDEs, from the ...


book review
Consciousness: an Introduction, by Susan Blackmore

Fascinating. I bought this book because I first heard of this author as a former parapsychologist. It's always good to read books by those whom you disagree...


email
Resolve a dispute through Email? with a friend, college, customer or your boss

When you are in an e-mail argument, it is very hard to get out of it again. This lens will tell you a few of the things to watch out for when trying to mend...


pizza
How do you know the cheese on frozen pizza is actually cheese?

A kid in The Netherlands asked the CEO of a food company some questions for a school project. One of those questions was: is the cheese on a frozen pizza really...


meditation
BodyMind Meditative Games Boundary In A Box

Boundary in a Box is a self-health game system that combines imaginative play with common body-mind healing practices and simple somatic (body) psychotherapies...


philosophy
David Bohm: science and spirituality

Famous for his 'Implicate and Explicite Order', quantum physicist David Bohm combines a knowledge of current day physics with a spiritual vision of the ...


heart disease
Going Red - women and heart conditions

Going Red! Are you tired of hearing the phrase? I hope not! Going red is the term used to draw attention to heart problems in women. Women die of heart problems...


scientist
Fascinating scientists and intruiging science

My lensography of fascinating scientists and their books. The scientists chosen obviously reflect my interests: religion, spirituality, philosophy and ...


healthy living
Health and Beauty Lensography

Health and beauty go together - at least: health contributes to beauty. Ultimately, for most of us, health is more important. What follows are my lenses ...


consciousness
Consciousness, Awareness, Psychology & Neurology Headquarters

For lenses about this puzzling topic - both debate lenses and teaching lenses are welcome. However interested I personally am in spiritual growth - this group...

More Art

Earth
Inspiring pictures of nature, photographs and posters

Enjoy the pictures of animals in their natural habitat and the scenery of nature. I feel this kind of photography gives a sense of peace to a home. Most of...


spiritual art
Alex Grey

Alex Grey (born November 29, 1953) is an American artist specializing in spiritual and visionary art. There is a clear connection with the world of alternative...


sell art online
Art, photography and puzzles...

My parents have three kids and I'm the least artistic. That's not saying much, because both my brothers aim to be professional artists. Between the two of them...


hinduism
B.G. Sharma

Bhanwar lal Girdhari lal Sharma (B. G. Sharma) is an award-winning painter from Rajasthan, India. He is famous for his miniature devotional paintings and his...


Best gift ideas
Best Beautiful Fractal Books

Fractals are a fascinating field of Mathematics in which patterns get repeated in ever smaller form. What's more, they turn out to describe very different...


art gifts
Best Fantasy Christmas Gifts, Top ideas for fantasy presents

Whether it's Lord of the Rings, Harry Potter or dragons. I've found posters, collectibles, t-shirts and comforters for you. From Twilight to Lord of...


home decorating
Best Islamic Art Gifts for Eid ul Fitr

An Art Gift displays class and refinement. Art doesn't necessarily have to be expensive. There are tasteful reproductions, posters, and calendars which wil...


buddha
Buddha Figures, busts and Buddhist statues

Buddha figures are everywhere. Buddha heads have become a fashion statement. Buddha statues, really just the next way to show off your spiritual inclination....


buddhism gifts
Buddhist Goddesses Art by Romio Shrestha

I got 'Goddesses of the celestial gallery' for my birthday (2010). It was quite a chore to take it home: it's almost as tall as this desk! (aka Poster size)...


orthodox
Byzantine Decorations for Christmas

The Eastern Catholic Church is one of the oldest Churches and along with the Latin Church forms the worldwide Catholic Church. Centuries old traditions have...


shopping
Fairies Posters Fantasy Art

Fairies, pixies, gnomes and elves... They stand for magic, imagination, creativity and mystery. Fairies particularly are popular because they are also thought...


fine art
FINE art or FOLK art?

FINE art or FOLK art? Fine art and folk art are so hard to define, that even wikipedia gives up on it. Still, fine art is for rich people, upper class, educated....


spirituality
How to make a mandala

Mandala's are an inspiring spiritual art form. You can get your kids involved with spiritual art in all kinds of ways - from simply coloring preprinted ...


folk art
Linda Nelson Stocks Folk Art

With art that reminds me of my favorite children's books growing up, it's no wonder Linda's art sells at several thousand dollars a piece. This page is mostly...


spirituality
Mandala Meditation Posters

An art form developed in India and Tibet, mandalas have come to be seen as symbols of inner peace and balance. These mandala posters are sometimes based on traditional...


marjolein bastin
Marjolein Bastin Checkbook Covers

You carry your checkbook around with you every day, but does it have to look so boring? Not if you use a Marjolein Bastin Check Book Cover to hold it. It's...


Home decorating
Marjolein Bastin Collectibles and Gifts

Marjolein Bastin has a love of nature which shines through in her art. She's a family person, with two grown children and several grandchildren. She was born...


baby pictures
New baby pictures, Cute posters and photographs

Who doesn't love pictures of babies? I don't know that anybody does. They're cute, they're cuddly and they give you that warm fuzzy feeling inside. I've found...


art
Salvador Dali - religiously themed surrealistic art

A madman? A genius? A surrealist painter, but also a realist painter. An atheist, but later converted to Roman Catholicism. Despite the many developments in...


fractals
What are fractals? Recursive geometry in nature

On the left you see a version of the most famous fractal of all time: the Mandelbrot fractal. However closely you zoom in, you'll always see roughly the...

Important!

Thanks for all your support!

A big thank you to all of you who've supported my online work by:

People talking about fractals online

'Fractal Zooms!' spiral and soar in NH
A musical kaleidoscope of morphing patterns and fantastic imagery will take visitors at the McAuliffe-Shepard Discovery Center beyond the blueprints of nature and into the ethereal world of imagination in ?Fractal Zooms!,? a new planetarium show ...
A Fractal A Day Offers 365 Snippet Of Infinity
But with fractals, confounding mathematical equations can become intriguing, self-similar patterns. So as you magnify a fractal, you'll simply see their details repeated again and again. Fractals are nature's data visualizer--or barber shop ...
App Detail ยป Fractal : Make Blooms Not War
From the creators of the award-winning games Auditorium and Pulse: Volume One comes Fractal, a new ambient music puzzler experience. Combo, Chain, and Cascade your way through a pulsing technicolor dreamscape that reacts to your every move, ...

by

spirituality

I'm a webmaster and student of religion and spirituality. See my website on religion and spirituality: www.katinkahesselink.net or my spiritual blog: All... more »

Feeling creative? Create a Lens!